Short Answer:
Basic Evocation Wizards are now the equivalent of Tier 3 at lower levels.
Basic Champion Fighters are now the equivalent of Tier 3 at lower levels.
The Usefulness of Tiers will have to change for 5e, as tiers 1, 5, and 6 at this time don't exist, and likely won't exist as the overall power of 5e is much flatter. We can compare classes by looking at their average DPAD (damage per adventuring day).
For overall power however, it's going to really depend on level.
Thanks to the work by @Waxeagle we can see how power via damage shifts over level.
Basically at level 11, the Fighter is doing more damage than the evocation wizard who is focused solely on damage. However, by level 17, both the cleric and the Wizard have enough spell slots, to out perform the Fighter and Rogue. In addition, level 9 spells are by their nature "game changers". It should be noted that at level 20, with the third extra attack, the fighter shoots up in power as well, though not enough to out perform spells such as meteor storm, the nuclear weapon of D&D. One caveate to the current graph is that not all levels are shown, only the level when the "adventure tier" changes. For example, not shown on the graph is level 10, where the fighter still only has one extra attack, the wizard and cleric are doing about the same amount as the fighter.
So while it is still the case at the highest levels that magic is more powerful than the mundane, up until the epic tier, this problem does not really present itself.
This obviously doesn't take into account the non-damaging effects of spells, such as haste, or invisibility, or flying, etc. However, with the new concentration mechanic, these spells are situational and can not be easily piled on top of each other as they could in 3rd edition, to create a quadratic power curve.
Relevant data for the chart:
The above chart is based on the various classes an unlimited number of enemies with the following defenses, and no assumption is made about the HP of the monster, so damage is "unbounded" in the terms of the spreadsheet:
Dex Save 2
AC 15
Con Save 2
However, If I change the defences of the monsters to something less reasonable in the game, such as giving a Dex and Con save of 5 and an AC of 10, we see the fighter keeping up with the wizard and again surpassing it at level 20.
You can compare these 5e graphs, to this 3.5 graph and notice how the fighter is at the bottom of the graph and stays very linear, while the wizard has a slight a quadradic curve in power gains.
(Graph taken from here)
Old Long Answer about Tiers:
First, the assertion that a Wizard might be tier 1:
Tier 1: Capable of doing absolutely everything, often better than
classes that specialize in that thing. Often capable of solving
encounters with a single mechanical ability and little thought from
the player. Has world changing powers at high levels. These guys, if
played well, can break a campaign and can be very hard to challenge
without extreme DM fiat, especially if Tier 3s and below are in the
party.
It's pretty clear that currently, the Evocation Wizard can not do absolutely everything. Because of the concentration mechanic, the Wizard can really only do one cool thing at a time. You can't fly and be invisible at the same time without another magic item or wizard casting those spells on you, for example. Secondly, while some spells can duplicate other class abilities, such as "knock", those spells are only situationally better, and come at a high resource spot (limited spell slots) that other classes lack. So the Wizard is no longer a tier 1 class.
Instead, I would say that Tier 3 fits the Evocation Wizard.
Tier 3: Capable of doing one thing quite well, while still being
useful when that one thing is inappropriate, or capable of doing all
things, but not as well as classes that specialize in that area.
Occasionally has a mechanical ability that can solve an encounter, but
this is relatively rare and easy to deal with. Challenging such a
character takes some thought from the DM, but isn't too difficult.
Will outshine any Tier 5s in the party much of the time.
The bolded part is why I believe a Wizard is Tier 3. A wizard can, if picked the right spells, do anything another class can do (with some exceptions), but it can't do those things as well as the class that specializes in that thing. An invisible wizard is hidden, but can't sneak. A wizard with damage spells, can't kill, a single high hitpoint target as well as a fighter can. A Rogue will have better skill abilities when it specializes in those skills than a wizard can ever get.
Next the assertion that a fighter is tier 5.
Tier 5 is defined by:
Tier 5: Capable of doing only one thing, and not necessarily all that
well, or so unfocused that they have trouble mastering anything, and
in many types of encounters the character cannot contribute. In some
cases, can do one thing very well, but that one thing is very often
not needed. Has trouble shining in any encounter unless the rest of
the party is weak in that situation and the encounter matches their
strengths. DMs may have to work to avoid the player feeling that their
character is worthless unless the entire party is Tier 4 and below.
Characters in this tier will often feel like one trick ponies if they
do well, or just feel like they have no tricks at all if they build
the class poorly.
No class is good at only one thing. Because of the Background system, all classes and characters are able to focus on skills that are outside of their class. So while you can make a fighter that is only good at fighting, and can't do anything during exploration or social interactions, it's also more likely to build a fighter that is good at fighting and leading people. Or good at fighting and using certain tools. Because of bounded Accuracy, all characters are decent at whatever skill they are proficient in. The champion fighter is best built for two handed heavy weapons, but they can also be a good archer, or duelist. Fighters excel in combat and at higher levels, can move across the battle field, hitting multiple creatures in one turn in the same way that a wizard might target more than one creature with a spell. They are also able to survive situations that others would not without a cleric. So I don't think they can be called Tier 5.
Champion fighters are however tier 3, because they are
Capable of doing one thing quite well, while still being useful when that one thing is inappropriate.
Fighters do combat really well, they survive well and can kill well. However sometimes a situation will be called where there is no combat. Fighters can excel at jumping across chasms, or climbing/swimming out of tough spots more so than wizards and clerics. With Background again, they can also call upon their traits. In the starter set for example, the Fighter is a folk hero, who is able to rally others to their cause.
However, the tier system as a whole is a bad way to judge D&D 5e classes. The power level of the entire system has been made "more flat", and there will need to be better definitions of how to compare classes.
No, Pathfinder actually makes the balance quite a bit worse.
The weakest classes got weaker, and the strongest classes got stronger.
Changes to combat feats and combat maneuvers mean that the few mundane tricks the system had, are now much more difficult to pull off and are less useful when you do.
Changes to magic items disproportionately hurt martial characters
Insistence on strict and painful “realism taxes” on mundane characters, even well into high levels, prevent them from keeping up.
Nerfs to spells were few and haphazard – while a few specific cases were nerfed considerably, most were untouched, and plenty of high-power options remain
Class features for spellcasters are occasionally quite potent. While some archetypes for mundane classes are also pretty good, the fact that the best classes could actually get substantial improvements is worrisome.
Combat Maneuvers
The math on Combat Maneuver Bonus vs. Combat Maneuver Defense is poor. Simplifying and unifying the systems was a good idea, but they failed on execution. Because you add both Str and Dex to CMD, but only one to CMB (and for several other reasons, this is just the simplest one), CMD scales much better than CMB does. As a result, at mid-to-high levels it becomes very difficult to actually use combat maneuvers.
Meanwhile, most of the Improved (combat maneuver) feats have been split into both Improved ____ and Greater ____: two feats to do what you used to be able to do in a single feat. In the most important case, Trip, two feats to not even do what you did with one in 3.5: now the follow-up attack off of a trip is an attack of opportunity, which means trippers require Combat Reflexes to use it, and need a lot more Dexterity.
Items
Changes to items are also serious problems to martial classes. All enhancement bonuses to a physical ability score are found only on belts – which means if you want more than one, you have to pay harsh premiums on combining items. Martial characters need bonuses to both Strength and Constitution (or Dexterity and Constitution in some cases), because the math of the system still has those bonuses baked into the design assumptions, but now they cost more. Compare this to 3.5, which, as of Magic Item Compendium, charged no premium to add these sorts of abilities even to other items entirely.
Meanwhile, while it’s also true that all enhancement bonuses to mental scores are headbands, most spellcasters only care about one mental score (Wis for clerics and druids, Cha for bards and sorcerers, Int for wizards, and so on), and then they are free to get a bonus to Constitution (most character’s second-most-important ability) without having to pay extra.
To add insult to injury, the official guidance on houseruling magic items explicitly says you should not allow these items in different slots even as a houserule! They were so adamant about enforcing this massive penalty on mundane characters that they literally called out DMs who were considering fixing it!
Realism Taxes
The most glaring example here, though far from the only one, is the insistence that, “just because it costs a feat,” i.e. a major character resource, doesn’t mean exotic weapons are supposed to be better than martial weapons. And, in fact, none of them are actually good. 3.5 had a lot of problems with Exotic Weapon Proficiency; very few of the exotic weapons were actually worth a feat. Pathfinder made very sure to nerf those so they no longer were.
Minimal spell nerfs
Depowering spellcasters really requires going through each and every spell; Paizo did not even attempt this. They did nerf a few particularly-notorious spells, but missed many others. They did nerf the polymorph spells, which desperately needed it, so that is a good thing; Pathfinder polymorphing is without a doubt a massive improvement over 3.5. But it’s also just about the best change in the entire system.
Further, they have printed new spells of absurd power. Do a google search for paragon surge and the ridiculous things that can be done with it.
Astonishing class features for spellcasters
The arcanist, a new Pathfinder class, is by-far the worst offender here, getting the best of both worlds between prepared and spontaneous spellcasting, off the best spell list in the game, plus free metamagic effects (read: one of the most powerful classes of effects in the game). But the core classes also occasionally got major upgrades as well.
By contrast, the default fighter gets a variety of small numerical bonuses. The fighter’s problem was never numbers – if a fighter can make his numbers count, you’re dead, 3.5 or Pathfinder. The problem was always that the fighter is remarkably poor at forcing his numbers into the game, if the competition didn’t actively cooperate with him. None of that changed.
This list is not exhaustive
This isn’t everything that Pathfinder did that exacerbated the mundane-vs-magic divide that was already massive in 3.5. It was, in fact, a very consistent effort across Pathfinder’s entire history. The Pathfinder FAQ and errata are chock full of the developers stripping away anything powerful or useful they accidentally gave to mundane characters. Pathfinder is therefore one of the most magically-dominated systems out there.
Best Answer
They have not fixed it, but it got reduced a little
The question about Linear fighters, Quadratic Wizards is a question about the balance between martials and casters. To summarize, while a martial gains a +X upgrade every level (+1, +2, +3, etc), a caster gains a +X^Y upgrade every level (+1 and charm, +2 and fly, +3 and teleportation, etc). To better understand the topic, the fine answers to this other question should be viewed first.
Spells are...Spells, and it's difficult to balance the creativity used to write new spells to "fighting better...somehow?". The versatility added with feats will never compete with spells until they decide that feats should be more versatile and do more than one or two things, or require multiple other feats. Spells are usually standalone and will do very well what they are proposed to do, with their effectiveness usually only being limited by the caster's creativity. It's not uncommon for players to find new uses for spells that were beyond the developer's imagination when he wrote it.
However, by reading all the classes so far in the playtest, watching some actual play podcasts and developer interviews, and frequently browsing the playtest forums, only one seems to be lacking both in the power potential and versatility, the alchemist. Fighters, paladins, rangers, rogues, and monks will do many more things related to being competent in combat, but little else outside of combat, unlike spellcasters in general.
The way things scale now in 2e brought numbers much closer together, as weapon damage will also scale up as you level up and spells will only scale in damage if you actually use a higher spell slot. But you won't see a fighter casting the equivalent to a fireball (which has limited daily uses) with their actions, even if they could do similar damage with a well-placed whirlwind attack, they get it at least 9 levels too late (14th vs 5th). The design idea still seems to be comparing unlimited uses versus limited uses to balance abilities between martials and casters. Martials get unlimited uses per day, while casters get limited uses with their spell slots, and as such, spells are stronger.
While at 5th level a wizard is already able to fly and rain 3d6 damage cantrips at foes for a whole combat, the 5th level fighter has abilities to hit two enemies at once or to gain +2 to AC until the start of their next turn.
But you said it got reduced? Yes, I did say it and it did, they merged many abilities from several feats directly into the classes, and those are all choices you can take (class feats). Feats are now more focused on skill usage and out of combat utility. Martials get many more options as they gain more combat-related choices while leveling up, but those are nearly always limited to combat utility.
The reliance on other feats is pretty much gone, you will get feat that makes previous feats better, but not completely different feats that require another previous feat that really has no relation to what the new feat does (like weapon focus and weapon specialization). For instance, a fighter that took Shield Block, (a reaction to raise your shield to absorb damage) can, later on, get Quick Shield Block, a feat that grants a free reaction that can be used only for shield blocking. Or a Double Shot feat can be upgraded to a Triple Shot, which works similarly but instead of using two actions, will use all three actions at a reduced penalty.
Think all the old combat feats baked directly into the classes now.
As for casters, while they do get way more utility in spells, the numbers of single-targeted damaging abilities are not that far from what martials can do. The DCs of spells got relatively reduced and will scale more slowly as they level up, on pair with how your saves will scale up too.
Spell scaling
Remember when I said that spells won't scale up unless you use a higher spell slot? That is a problem often pointed out in these discussions about Quadratic Wizards, and let me try to explain.
In 3.PF, when a wizard levels up from 5th level to 6th, not only they gained an extra use of fireball, but their fireballs also got stronger. And this was even worse when they would gain new spell slots, as they could prepare their low level spells into higher level slots for the same effects (instead of 4 fireballs, you now can cast 7), but also had the benefits of using metamagic feats to increase the spell effect even more.
This passive scaling is gone in 2e for every spell but cantrips (just like happened in d&d 5e) and powers (which are similar to supernatural and spell-like abilities). To increase the damage output of your fireball, you gotta prepare the spell using a higher level slot. But this isn't exclusive to damaging spells, mage armor will start at +2 AC and get +1 AC for every slot level above first, healing spells will increase their number of dice by using higher level slots, and utility spells will allow you to affect more targets, or increase their duration (from 1 minute to 1 hour), or cause a stronger effect that has a broader utility (from humanoid creature to any creature), or even changing the possible targets (from Personal to Touch).
Casters still grow exponentially more useful and versatile for every extra level of spells they get, but their older spells won't automatically scale up when they learn new spells. If used on the same spell slots, they will remain with the exact same power they had when you first learned those spells.
While metamagic feats are still a thing, those known for causing balance issues, like empower or maximize, are gone. Quicken, a major offender, is still in the game, but is limited to once per day, will actually reduce the number of actions required to cast the spell by one, and using a free action, you will not be able to combine it with other metamagics. We don't know if those will be back (as we know them) in future supplements though.
Action economy
Now, regarding the action economy, the game is far more balanced now. Weaker spells cost an action, strong spells cost three actions, and everything else is pretty much in the middle at two actions. Meanwhile, martial abilities are mostly one action, sometimes two, which will have some added combat utility to it. A single cantrip or magic missile will cost a caster two actions, while a martial can usually make two attacks with the same two actions.
All characters begin the game with three actions, which can be used to move, make an attack, switch weapons and so on. This helped reducing the reliance on iterative attacks that caused so many headaches to martials. Instead of granting more attacks as they level up, their attacks are better, the penalties for additional attacks are reduced and they can apply debuffs with those attacks.
We also have additional combat effects baked into weapons, such as being able to cleave when you critical hit with an axe should your character be specialized on axes. Or even simpler abilities like reduced penalties when making multiple attacks with that weapon (agile), or a bonus when attacking an adjacent enemy (sweep), or even a bonus for making multiple attacks in a sequence (forceful).
Magic items
Another problem that plagued martials and didn't really bother casters was the fact that it was much harder to upgrade two or three different ability scores while casters could focus all their attention at one ability. The mandatory magic items required for all characters are completely gone, and while you may still have items that grant +X to certain skills, and others that grant either +2 or X value to a certain ability score, those items are no longer necessary to keep your character balanced against enemies. Bonuses to saves, AC, and attacks will happen naturally as you level up, allowing characters to focus on utility magic items in those body slots. The dreaded cloak of resistance and amulet of natural armor are gone.
A Belt of Giant Strength, for instance, will grant you bonuses to athletic checks (+4), bonus to break objects, grapple or get out of a grapple (+2). And finally, if you invest your Resonance (a resource used to fuel magic items with a limited daily pool), you can either get +2 to strength or get a strength score of 18, whichever is higher. Additionally, you may be able to use your reaction to grab a rock thrown at you.
Ability Score Boosts
All those +X bonuses that before came from magic items are now granted as you level up. Each character will gain four different ability score boosts, which are translated as a +2 bonus to a chosen ability if it's not yet at 18+, or a +1 bonus to that ability if it's already at 18+. So, even if the wizard does focus on a single ability, they will have three other abilities that they will be upgrading at the same time, just like the fighter. So, it's possible to have high ability scores on all necessary abilities even if you have no access to magic items at all.
Those boosts are granted every 5 levels to every class, meaning that the game will try balance itself in 5-level increments, expecting all classes to have roughly the same numbers regarding their attack rolls, defenses and skill bonuses.
But as this fine answer explains, it's still too early to have any definitive answer on this subject, especially since they are still playtesting mechanics, and even things like core mechanics (like how alchemists work) are being updated weekly.