[RPG] Is there enough disparity between the classes to put them into tiers

These are bascially listed in order from “smallest and easiest” to “biggest and hardest.”

Step One: Eliminate the lost spellcasting level at 3rd

There’s literally no reason for it. At the time, it may have been believed that there were advantages to spontaneous casting that demanded it as a balancing factor, or, as rumored, Monte Cook may have just hated sorcerers (see here for a search for the real reason), but experience and hindsight have demonstrated it to not be the case.

Step Two: Rapid Metamagic

One of the natural and fitting advantages that spontaneous spellcasters should have is the ability to apply metamagic on the fly, but the increased casting time for this ruins that. So eliminate that.

Step Three: Consider More Spells per Day

This is the advantage that spontaneous casters have, but the difference isn’t all that large: usually about 1 spell per day per spell level. It could be bigger, to make it worth a little more. That said, spells per day is rarely a meaningful limitation on spellcasters past level 7 or so (and even that might be generous).

Step Four: Consider More Spells Known

It definitely reduces a major stumbling block for them, and considering that prepared spellcasters have spells known of “all the spells,” they aren’t likely to be threatened by it. For example, sorcerers know spells in a distribution very similar to the wizards spells per day, which means that the sorcerer has to “prepare” the same number of spells as the wizard, he just has to prepare for the rest of his life while the wizard only has to prepare for the next day.

Bonus: Sorcerer specifically

The sorcerer really deserves a better chassis and class features. 2 + Int skill points, on a Cha-based class? That’s just mean. For that matter, a Cha-based class, with only Bluff as a Cha-based class-skill? Why? Give them Intimidate, at the least. Some more knowledges would not be amiss. And some class features, even if it’s just Eschew Materials at 1st and bonus feats as the wizard gets. Some of Pathfinder’s bloodlines are ridiculous, but some of them are fair enough.

Breadth of Option

Unexpected monster rears out of the darkness, clearly well beyond the battered party's ability to handle?

Wizard teleports home. Fighter manages to kill the thing half to death before he gets eaten.

Ambuscade! The earl's men have the party cornered, and demand they surrender - only execution awaits if they do.

Wizard casts glitterdust - blinding most of the enemies and allowing his comrades to cut them to pieces. Or he turns invisible and leaves them to their fate. Maybe he uses a colour spray, and stuns half of the enemies, or burning hands to kill a different half. Maybe he runs away, and leaps off a cliff while casting featherfall. Fighter faces down 15 halberds and hopes to god his HP and AC hold out long enough for his Cleave feat to cut through them, because other than hoofing it, that's his only option.

It's less true, but still prevalent, at low levels, that Wizards can escape or defeat situations that kill fighters. At levels past 7, though, once Wizards get vastly more powerful options, foes become deadlier in melee than the Fighter, and Wizards can prepare enough spells to prepare for many different circumstances, the gap widens enough that the two classes are, barring self-nerfing/DM hand on the scales, playing different games.

The arguments against this generally incorporate self-nerfing. I've personally had first-time players pick the better spells on the wizard spell list, reliably. Animate Rope is indeed a wizard spell - but new players can easily see that it's utility compared to Burning Hands is very low. Fire Trap, Detect Scrying, Dimensional Anchor, Arcane Eye - all have uses, but new players pick Polymorph, and some of them even turn into hydras. Literally first-time players. There is a wide-spread culture of casters intentionally playing weaker than their class options offers them, especially amongst 'traditionalist' DnD players. This is to avoid GM banhammer/fudging the rules to smash them, generally, and has dated back to the earliest days of DnD.

Wizard spells are stronger than fighter options for less action economy (standard vs Full-Round), they can use them from range instead of their best tricks requiring melee, they can target groups, single targets, saving throws, hp, AC, no save at all,line of sight/effect blocking, creating minions, destroying enemy weapons/shields, altering the battlefield, and decide which to do on the fly instead of needing feat chains (that are still inferior to spells even if you have them), they can layer buffs to be tougher in every way than a fighter, they can use spells to be faster in every mode of movement than a fighter, they can literally see things before they happen and set up the perfect counter, spy on people from far away, turn enemies into allies, read minds, solve every single kind of encounter, create armies of minions (even without cheese, the literal lesser planar binding spell, the literal Dominate Person spell), turn into a gas and slip through the keyhole of doors, you know, whatever they like.

The sole 'downside' for this real ultimate power is that they can only use so much of it before needing a naptime. And since they can teleport home, or use spells to secure a safe place to nap, and since killing defenseless parties is kind of a dick DM move, in effect this is not a big deal without time pressures. And even if you can consistently use time pressures without it negatively impacting the story, you still have to effectively read the wizard's mind - as without his spells being used, an 'easy' encounter can swiftly lead to a TPK (at least, of the non-teleport/invisibility/gaseous form capable members of the party). Which is again bad DMing.

Individual wizards might self-nerf into being fighter-level, but the wizard class is a powerhouse of might. It becomes godlike, odin or zeus while the fighter stays firmly in hercules territory. But even at low levels, the wizard has options the fighter doesn't, and at everything but 'random damage comes out of nowhere! you take hp loss' has choices that will keep him alive instead of choices that lead to him relying on dice rolls against AC in order to not die.