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.
Mechanical
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.
Setting
In ArM3, due to a desire to be [somewhat compatible][1] 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.
Setting
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.)
Mechanics
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.
Best Answer
5e is about as different from Pathfinder as 2e is from 3.x. 5e is trying to bring back certain aspects, most notably the particular AD&D brand of soft-rules + rules-heavy rule paradigm, from the AD&D/D&D 2e line that weren't present in either 3.x or 4e.
See also the excellent top rated, accepted, and bounty-receiving answer by @mxyzplk. Basically, as predicted, 5e reincorporates a lot of the 2e philosophy into the game. The answer does seem to suggest that 5e is reincorporating 3e mechanics as well, but I think that's actually more of a 4e being off in left field thing and 5e going back to mainstream D&D in general than anything distinctly 3.x that had been removed being brought back.
If you like Pathfinder, particularly if you like the mechanical complexity, I would not recommend 5e to you. If you're looking for a modern version of OD&D I would definitely recommend it. Basically, don't think of it as a sequel to the game system you currently play, think of it as a completely different system that's also D&D and happens to have a lot of similarities.
Use Pathfinder
if you uphold US copyright law and can't abide non-PDF rulebooks. Wizards isn't planning on releasing ebook copies of 5e material at any point in the foreseeable future. This also might change, but isn't super likely.
If you like mechanical complexity over ease-of-use. 5e has an advantage/disadvantage system that is intended to replace the bonus system found in 3.X. It's very lightweight and easy to use, but the maximum modifier from (dis)advantage is approx. ±5, and there is no 'more' or 'in-between'.
If the GM not making up/ignoring/modifying rules is part of your gaming social contract.
If you want a complete ruleset, in the sense that the rules provide at some level for all player actions and RAW gameplay is supported/encouraged. D&D 5e will never be 'complete' in this sense because that is not an aim of the developers.
If you want highly customizable characters. Characters in 5e have very very few twiddly bits, especially at low levels, and almost no multiclass builds are viable (even compared to Pathfinder, which isn't exactly multiclass-friendly). Characters in Pathfinder have between 'a lot' and 'more than that' choices to make, even at the lowest levels.
Use 5e
If you're looking to play an old-school-style D&D game but don't actually want to deal with old-school mechanical stuff like class-based To-Hit look-up tables and want the 'official' D&D version for such a game, as opposed to one of the 3rd party retroclones.
If you like AD&D 2nd edition and are interested in trying out something similar but new.
If your group believes that rule sets exist as a tool to teach people how to GM or as a basis for GM development of an actual rule set for use in play, and as such the RAW should never be used to run a game and may even be wholly insufficient for doing so.
If you want to play D&D, don't want to put too much time or effort into understanding a rulebook, aren't particularly good at math, want gameplay to go quickly and smoothly, and don't like 4e for some reason.