Just picked up the game today, and spent about an hour with it. The best way to describe it: it's just the Spider-Man sections of Ultimate Spider-Man, but with touchscreen controls instead of using buttons. There's much more to it of course, but that's just the easiest way of summing it up.
Honestly, while the touchscreen controls work, I wouldn't mind having the buttons back. While the control pad/touchscreen combo is easy enough to use, there's just some times where I would have preferred to use buttons. The system is pretty cool though, and it can be learned pretty quickly. Walking and webslinging is controlled with the control pad, while everything else is done with the touchscreen. All you do is double tap the screen to shoot web, slash the screen in certain directions to punch, kick, and throw enemies, etc.
But yeah, most of the stuff you did in Ultimate Spider-Man is here as well. You still beat up random thugs, you still have to save people from fires and such by taking them to a safe area, you still have boss battles. It is a little less linear than USM, as you can just choose to freely roam around the city instead of progressing though the story, but in the end the game plays similar to it. Of course, none of this is a bad thing, as USM was an awesome game.