Long time player of ArM5 here, with my recollections:
3rd edition to 4th
The largest differences are those not listed on page 262 of ArM4 Core. The publisher changed from White wolf to Atlas and therefore the fundamental assumptions behind the game changed.
The largest change, in my opinion is that ArM4 has "spell boosting" where you can burn vis for an extremely non-trivial range, duration, or target increase. This changes the balance of power of magi in mythic europe.
In ArM3, due to a desire to be [somewhat compatible] with other white wolf products, there's True Reason as an Aura and virtue that's pretty silly. Basically it's taking enlightenment concepts and trying to push them back in time. House Guernicus is known as Quaesator, due to their most common role. Virtues and flaws have a different balance. There's a link between Tremere in ArM and Tremere in WoD. Confidence operates as reroll instead of bonus.
I'm sure there are other, subtle, differences, but the largest are in the feel of the setting. The difference in publishers makes a significant change to the tone of the game.
4th to 5th
The differences from 4th to 5th are, as the core book says on 223, "Nothing has changed ... Everything has changed" And it's completely correct. The setting changes from 3rd to 4th are mostly gone, though with a few humorous notes: "The Tremere had a problem with vampires. They fixed it. It's not interesting now." Which is riffing on the white wolf stuff.
Functionally speaking, there are no setting changes that I can tell, and I'm quite familiar with 4th and 5th. While it's possible to use setting books from any edition due to the... rough familiarity of editions, setting books from 3rd and below require "interpretation" that books and adventures from 4th don't. Adventures from 4th are almost wholly compatible, due to the whole "monsters have built-in powers" things. When adapting adventures, power down the opposition, but they can be run from the books as-is.
The largest change in setting comes from the supplements (Art and Academe is a must buy for anyone interested in that time period. City and Guild is a horrible supplement.) There is a much lower focus on "magic" in the world and more focus on the world qua itself. This complements the absence of vis-boosting which means magi cannot trivially take out mundane armies, especially with Realms of Power: The Divine in play. The world as presented is open to significant amounts of interpretation, just like in earlier editions, which suggests the ability to dial for whatever game you want to play. (My current game is mostly focused on resource management and survival in a hostile political atmosphere, and I'm happy to share how I figured out highly-granular accounting schemes for the covenant in a different post if poeple are interested.)
One of the more striking "everything changed" aspects is in virtues. The point system (thankfully) was abolished and virtues consolidated into major and minor. With the exception of Beserk (minor virtue, should be major flaw in how it works out in game play) there are no "trapped" virtues or flaws like previous editions sported. Spell Guidelines have been rationalized and consolidated very well, tough the ranges, durations, and targets have changed slightly (for the better.) There are fewer ones, but spells are roughly at the same power level. Vis is far far less useful in spellcasting and rituals generate long-term fatigue, so they are profoundly not spammable. The changes guide is an excellent reference due to the lack of setting changes.
One of the larger mechanical changes that will impact how players think about the game is confidence. In 4th ed, if you had enough confidence, you could spend it all on every roll and, barring a botch, always succeed and get it back. In 5th, confidence is split into Confidence Score and confidence points (and roughly each realm has an [Hierarchy (Infernal),True Faith(Divine),Fable(Faerie)) score to reflect increasing affiliation with that realm. The magic realm doesn't have a unique one, which reflects the centrality of the core book. Players earn confidence points by role playing and can spend them (as the rules are written) on any stress die roll that happens for a specific event. I run with the house rule that confidence can be spent on anything, which significantly ramps up the rate of power increase.
Combat is lethal, but sane. The rules reward armor and big weapons.
All lab work uses the same mechanic, making it far easier to conceptualize what one is doing in the lab.
To summarize: 5th is more refined and an excellent revision to 4th. It streamlines and "balances" (not in terms of nerfing, per se, but a rationalization of equivalent power). It's quite feasable to port over a 4th edition game to 5th without any real prep. It would not require any significant editing of the world like a 3rd to 4th would have.
The two games are very different, despite sharing the same underpinnings. I know plenty of people who played previous editions who don't like 4e, and I know plenty of people who played previous editions who loved 4e. Hopefully we can navigate these rocky, contentious waters without flames.
First off, 4e is fairly light on non-combat rules. This doesn't mean that 4e games are all about combat; it means that the rules assume that a lot of the roleplaying activities that were codified in 3e will be done via freeform roleplay. For example, there aren't any crafting rules for anything other than magic items. There also aren't any general professional skills, and there aren't any NPC classes. If you prefer to have rules for that sort of thing, 3e will be a better choice for you.
Second, 4e uses a power-based design methodology. Classes can be thought of as collections of powers; the differences between classes are defined by the different power choices they have. This makes for a very modular and flexible system. Some people find that it makes the classes overly homogeneous; some people like it.
Third, every 4e class uses powers. That's implied by my second point but it's worth mentioning specifically. A character begins with two at-will powers, that he can use whenever he wants; one encounter power, that can be used once per fight; and one daily power, that can be used once per day. Even martial characters, such as warriors, use this paradigm -- although their "powers" might be better thought of as something akin to a martial arts kata. This was intended to make combat more interesting for (say) fighters, in comparison to the earlier model where fighters just tended to hit things over and over again. If you didn't mind that model, this change may be unnecessary for your play style.
Fourth, 4e leans more heavily on the battlemap. My impression is that the large number of movement-oriented powers both make the battlemap more important and make combat more fluid, but that's definitely a subjective opinion on my part: consider it something to think about if you try 4e rather than a definite fact.
Fifth, 4e introduces the concepts of roles. Roles are a way of classifying classes by what they tend to do in combat. You've got leaders, who heal. There are more of them than just the cleric; for example, the bard is also a leader. You've got defenders, who control the battlefield by encouraging enemies to focus their attacks on them. The fighter is a defender; so is the paladin. You've got controllers, who are somewhat difficult to define, but you can think of them as the classes that affect the flow of a fight: they can hamper enemies, reshape terrain, and so on. The wizard is a classic controller. And, finally, you've got strikers, who purely focus on doing damage. The ranger and the sorcerer are strikers. Every class is primarily one role, but every class has the ability to take on aspects of another role, depending on what the player wants to do.
Sixth, multiclassing is more limited than in 3e. You can multiclass in a couple of ways, but you don't get the same ability to take six or seven classes/prestige classes during the course of your career. 4e classes are fairly flexible, but you don't get the same complete freedom you would with 3e multiclassing.
Seventh, the scope and feel of 4e can be somewhat more epic; or, to put it differently, more broad. The highest level is level 30, and that's very epic play, with abilities that allow characters to come back from the dead. Even at level 1, your characters are significantly more durable than third edition characters, and they'll be able to pull off some really wild things.
I think that hits most of the major differences. It's good to remember that it's still a heroic fantasy game in which characters fight monsters. It still uses a 20 sided die. Also, if you want to try it out, WotC has a free Quick Start kit available.
Alternatively, the new Essentials Red Box will be out in a few weeks; at $20 US, it might be a good way to take a peek at the game and decide if you like it. The Essentials core books will present a bunch of new class variants that change some of the things above: e.g., fighters won't have the same power structure I mentioned. So that might be a better entrance point.