It's not great. It's pretty much a brainless summer action movie. I could dismiss it as that, even damn it with the faint praise of 'pretty good for a movie based on a video game,' and the acrobatics are entertaining.
But I can't say why I hated the movie without spoiling the ending. So here goes (in the most generic terms I can come up with): Throughout the movie, there's a mystery around a magical artifact, and if you do a certain something with it, it can destroy the entire world. And in the end, the villain does just that, while the hero tries to stop him, and...instead of destroying the world, it puts the hero in position to save everything.
You know, I'm so worked up about this, I actually retroactively hate the "cross the streams!" ending of GHOSTBUSTERS.... Ah, who am I kidding, I can't not love GHOSTBUSTERS. PRINCE OF PERSIA, on the other hand, sucked.
Oh yeah, and as for the time travel logic (I guess that's another big spoiler)--it's branching world logic, so kind of "meh." No big inconsistencies, because they didn't even try to address potential time travel paradoxes.