It does some things right, and some things wrong, unfortunately. People have complained about the vehicle handling, which yes, is pretty lousy, but on the other hand, you hardly ever need to use one.
The world map is huge, and very pretty, but it also doesn't feel as densely packed as JC2's. Not only that, but the addition of the wingsuit, while my favorite part of the game by far, actually ends up making everything feel smaller somehow. it took a while to get from one place to another in JC2, but while zipping around in the wingsuit isn't as fast as a jet, it's still really fast, so you don't get the same feel for the size of the islands. It also doesn't help that you more or less start with it, so you don't have that period where you're forced to get around with the parachute+grapple+vehicles, then you can suddenly appreciate the new toy you get.
People have complained a lot about the upgrade system, but I didn't have a huge problem with it. Yes, the cars handle like garbage, but you only need to use the cars for car-based upgrades, so I just ended up ignoring most of them. Not only that, but the gear requirements aren't super strict, so you can go around and get a few unlocks just by two-starring races. I actually liked most of the other mini-games. They're all fairly reasonable in difficulty, and pretty fun to do. As others have said, the wingsuit challenges are easily the best, simply for the Pilotwings vibe. Bonus points for actually being completable with a mouse+kb.
I think what bugs me the most about the game is that it feels like you're playing with mods, when it comes to Rico's abilities. You ever play a game and install some mod that makes you way, way more powerful you should be? That's kind of like what JC3 feels like. There's this weird mismatch where Rico's way more powerful than he was in JC2, but they didn't beef up the rest of the game to compensate. The enemies are, for the most part, your standard assortment of soldiers+tanks+helicopters+boats. There's one mechanic that's introduced about halfway in,
that made me think that they were going to be really beefing up the enemies from that point on to give man-god Rico more of a challenge, but alas, not only was that the only noteworthy addition, but they also don't really do anything with it.