PF2 quick highlights:
Action economy. You get three actions and can spend them however you want. Attack three times? Sure! (Note: there's a -5 penalty for the second attack and a -10 penalty for the third attack on the same turn (note: some feats can mitigate this eg. one that drops them to -3 and -6 respectively)). Move three times? Yeah! Move attack move? Attack move attack? Cast a spell (typically consumes two actions) and then attack? Sweet. Got a feature on your spell where you can funnel more actions into it for a bigger effect? Very cool.
Degrees of Success: Roll more than ten below the DC? Oof, that's not just a miss, that's a miss where you also fall on your ass. Ten or more over? That's a critical! You get sweet (and clearly defined) bonus effects. Roll a natural 20 or 1? That bumps you up or down a success tier instead of being an automatic failure or success. You might just be turning a critical miss into a regular miss on a 20 (given extreme DCs) or even a regular miss into a hail mary shot, like Bard hitting that gap between Smaug's scales.
Counteract as a broad mechanic: Counterspell is now just one implementation of a greater and robust counter mechanic, wherein you make a bid and possibly get a better result. The counterspell example is that you can counter a spell of up to three spell slot levels higher than the one you spent just by rolling high (see degrees of success above). This is also how you disarm traps and dispel auras.
Counterspell itself gets way more granular. It is very different depending on which class you're pulling it from, which means it feels way more satisfying, not having been smashed into a one-size-fits-all shape. You can build it up with feats, playing with the resource economy and requirements. My personal favorite is a feat which allows you (GM's discretion) to counter spells with thematically relevant spells, like fizzling a fireball with create water. It's intricate, it's interesting, you get way more control over your kit, and you get to feel really cool when you do cool stuff. Which applies to the system on the whole.

There are consistent rules that are written out pretty verbosely. This can be scary at first but also ‘generally’ prevents a lot of table discussion. There are tons of characters choice and it is pretty hard to make a low power/high power character; also encounter/monster building rules actually work. Price of this is that there are a lot of options that were balanced out of their fun. Thankfully they have been getting better at this.

Personally I think 5e sits at a weird point. There are games like PF2, 13th Age, etc. that deliver better gaming frameworks with depth and there are better ‘simple’ games like WWN and numerous retroclones that provide the bare minimum and empower GM to improvise. Where as 5e has had an approach more like the former to the rules interpretation and character complexity, with tons of unofficial official rules clarifications and specific character, while having the actual rules written out more like the latter group providing very little guidance to how to use them. It awes with fun abilities yet provides little on how they interact. It is not a bad game if the GM knows what they want out of it, but most games I have been in was a disparate mix of ‘things others do’. A lot of the blame lies with the DMG.