Neonchameleon
Legend
I dragged out my 4e books to take a closer look at powers, and yes, while there is lots of shifting, pulling and shoving, there are also a lot of very cool flavourful powers. The monk, for example, is way more interesting than the 5e monk. The game is more fantastical, especially when you add in the other player books. We have characters briefly turning into flights of birds or raining down shards from their bows, at 1st level.
I was not a fan of 4e, but taking another look, I think there's a lot there to commend it. Weapon choice is more meaningful. I've always liked the at will, encounter and daily idea, as it is nice and obvious when abilities can be used, and you don't have to rely on short rests.
There was a lot there and a vast amount of flavour. On the downside it's pretty heavily buried and the books are designed as reference manuals rather than something that's inspiring to read. Which is pretty ironic as thanks to the character builder and a clean ruleset with few fiddly exceptions they find less use as reference books than e.g. 5e rulebooks at the table.
As for the shifting, pulling, and shoving, I like being able to customise my fighter's fighting style and movement. How you move and how you attack makes you a lot more distinctive than a +2 here, a +3 there, and a 1 in 20 critical chance. I don't find it at all uninspiring but I do find it appeals to a certain type of kinaesthetic mindset while others like either faster options or more flash. Which is fine as both exist (and one reason I'm more keen on Essentials than a lot of 4e fans). And yes the PHB is the most vanilla book of them all and they got wilder in the supplements.
I also have every sympathy with someone who looks at the PHB ranger and finds it pretty boring. That class was popular because it was at the top of the power curve - but it wasn't interesting and was mostly a combat-blender.
As far as the character sheet being too complicated? You don't need a program. It's just going to be a lot of erasing when you level up. You are going to need power cards, however. No way all those abilities will be easily memorized. But, then again, I use them in 5e too (my own, not going to buy them.)
As mentioned I designed an entire 4e character on scrap paper with no books handy. And didn't make any mistakes. But to quote Jurassic Park "Just because you can doesn't mean you should".
The rules books are not immersive, which is odd because of its more fantastical feel at the table. It's not going to fit in with the typical adventures, we imagine in D&D, but if you want to play a game with mighty heroes, heading for fantastic destinies, who'll have a huge impact on the world, 4e is a good choice.
Honestly I find that 4e works really well with any sort of adventure path style adventure - although pretty badly with Fantasy F---ing Vietnam and DMing a 4e sandbox takes significant skill. 4e also does the best low-magic fantasy of any D&D because you really feel the lack of spellcasters in any other edition. In 4e you just say "Martial and near martial classes only. If you're going to play a Barbarian be sensible and don't take the options that are so metal that when you roar with your voice of thunder the heavens answer with lightning please". (Note: Not an exaggeration and you can start doing that from pretty low level).
But a big difference in tone is the one mentioned by @Xetheral above. In most editions of D&D magic is something other from the rest of the world and things are either magical or mundane and never the twain shall meet. The only genres of non-D&D fantasy where this applies that I can think of are Urban Fantasy (where our protagonist steps from the mundane world into the magical world) and Isikai (likewise but a very different magical world). In even the stories on which classic D&D is based such as Lord of the Rings, Conan, Jack Vance's Dying Earth, and Fafhrd and the Grey Mouser, things just are. The world is fantastic and the protagonists are larger than life even if they are normally not spellcasters (see above with 4e being the only D&D that can take an all non-casting party in its stride). Also explicit spellcasting is rare; someone notoriously worked out Gandalf was fifth level - and in Jack Vance's Dying Earth an archmage might be able to remember six spells at a time, but only the greatest of archmages.
As far as PF2 and 4e? The games don't really play the same. PF2 still feels like PF1. There are some similarities to 4e, but not to the extent that Paizo deliberately chose to copy 4e.
My hypothesis is that the only people saying PF2 is like 4e are those who neither like nor understand 4e and want to put two things they dislike into the same box.
The thing I haven't seen (and would be interested to) is some reason it's worth it to wade through character creation to get to the game. And what PF2 does better than anything else I've got on my shelf.