Both games are excellent, but Just Cause 2 offers more bang for the buck. You have a huge map to explore, four large sets of missions, and tons of easter eggs to find. There's a lot to do aside from blowing up all locations, which itself will take quite some time. Conviction is worth playing, but 80% of the game revolves around co-op, so if you don't have a friend to play with either online or locally, then you're stuck with the single-player (which is pretty fun, but not as good as the co-op levels). I'd rent the game unless you can get it really cheap.
Mirror's Edge is fantastic. The freerunning is so amazing, and the presentation of the game is great (art style and soundtrack). There are time trials to do, as well. The story is weak, but it's no big deal. My only gripe is that the combat kinda svcks, and it becomes mandatory towards the end of the game (usually you can just avoid enemies or quickly take them out with a slide kick or a flying kick, but towards the end there's a lot of unavoidable gunplay). Still, it was one of the best games of 2008, and at the current price, you've got no reason not to pick it up. If you have a PC, get that version since I think it supports custom levels (mods).