I'm not a huge fan of games where they tell you whom to play. That said, that's my main grudge against P2 -- you can't really choose what your character looks like, what his backstory is, etc. etc., and the fact that like in P1, it isn't really anyone too likeable doesn't help.
The control scheme now lets you choose two active powers versus Prototype 1's one, and while that sounds nice (especially the option to assign a slow move and a fast move, or a close range one and a long-range / area one), I didn't really find it all that useful in the game (I would assign one fast, close range attack as primary power and use it 95 % of the time, and have something like tendrils -- or later whip fist -- as a secondary for the rare cases where I needed to attack a helicopter or needed an area effect. Using each roughly 50 % for great synergy? Not so much. But maybe, that was just me.).
The downside is that while you get twice as many active skills, you have to handle them with the same number of buttons on the controller, and the controls feel less precise than in P1. Ironically, the most annoying issue wasn't even attack related; if you don't get quite the right attack, but still an attack, it's usually non-catastrophic. What I did get often enough for it to be a nuisance however was being on a stealth mission, pressing (B) to interact with some hapless soldier (usually to consume them and gain their memories; sometimes just to stop him keeping an eye on the person you came for), and instead prying lose some feature of the landscape that also happened to be close (but didn't even necessarily look like you could interact with it). And well, prying lose random ACs or oiltanks or whatever automatically raises an alert and ruins the stealth part of your mission. (This can also be an issue during melee, where you get a prompt to press (B) to consume an enemy who's been weakened enough, but who may die soon, and where in crowded locations (B) will then often select bystanders seemingly at random, all while your actual target is bleeding out.
I liked the skill system in P1 better (get XP for everything, then once you have enough XP to improve whatever skill you're interested in (i.e. buy many minor things quickly, or save up for big improvements)) vs P2's "you'll level up again at so-and-so many XP, and every time you do, you can improve exactly one skill", but in the end, it wasn't a huge factor.
(That said, the thing where you can get a skill buy eating the brain of someone who has it still exists.)
Unsurprisingly, the city looks much better than in P1; the player character looks much better, the voice acting is decent this time, and most of all, while there are certainly repetitive elements (mostly the Blacknet assassinations, which often don't have much in the way of plot -- this is even lampshaded one time: "So this guy is an APC driver? Doesn't really sound like a big bad mover and shaker ... ah, whatever, I'll kill him anyway."), the game, especially the main quest, feels much more like a story than the first game did at the best of times, and a sense of urgency is upheld at (almost) all times. Like a soap opera or Baking Bread, it isn't necessarily the cleverest plot on earth, but each mission creates enough of a cliffhanger to make you wonder what will happen next, and it's tremendously easy to get sucked into "just one more mission before bed."
As a bonus, much of the optional "color" of the setting is now told through audio logs you can find (and listen to while you move along), rather than flickering memories with corny visuals that don't really blend with the rest of the game and that interrupt your flow like in P1. Small change, surprisingly big effect. (Technically I guess they're a cross between the landmark orbs and the "color" memories of P1, but I played P1 and P2 in the same week, so it's becoming a bit of a blur.)
There are challenges and mini-games and somewhat repetitive kill zones, but unlike in Saints Row IV, they're not mandatory -- you can do one once in a while for variety or XP, or do them after the main quest for something to do with your then near maxed-out powers. Or, you can ignore them completely, and just do the main quest. Your choice.
The gliding, especially once upgraded, still won't carry you as far as SR IV's, but it feels world's away from P1's, which never felt much better than plain old falling.
A big plus: Starting maybe 2/3 in, P1 would just try to overwhelm you -- gliding was practically useless, perhaps in an attempt to keep you at street level, and at street level, there'd be a constant barrage -- even if for once, zombies weren't attacking you and soldiers weren't detecting you, you'd frequently ragdoll all over the place simply for getting caught in random crossfire of the marines or blackwatch using tanks and rockets at street level. Yes, it sounds good on paper -- getting swarmed is obviously very much a zombie trope, and the careless use of artillery demonstrated desperation / casual disregard for any survivors, but in reality, it just makes for a really unfun game mechanic when the true challenge of a misison isn't Doing The Thing, but getting there to do the thing. Meh. (This was exacerbated by the fact that using any speed powers could get a strike team called on you.) In P2, you get caught in the cross fire much less easily, you don't get swarmed by the zombies as much, strike teams aren't called in as easily, take longer to arrive, are easier to shake off, and are easier to kill. Heck, it's almost too easy in P2, but I'll take that over P1's traversing the city being a chore any day. P2 has "joy of movement!" :)
If you can stomach playing a character that they picked, rather than one that you picked, give it a go, especially if you've played part one, but get it while it's on sale. (It seems pretty much too late to vote with your dollar anyway, now that they've already downsized Radical -- which is actually a shame, I would've been interested in seeing how a Prototype 3 would've come out.)