I own both from earlier sales.
Batman is a great game. I played for a couple hours months ago, and just started getting back into it last week. It controls just fine with a keyboard and mouse. They did a good job with the default key mapping - everything is easy to reach. A lot of third-person action games control strangely on PC and work better with a gamepad, but I actually found Batman AA to be better with a keyboard and mouse. Either one works though.
Just Cause 2 is a lot of fun if you just want a wide open sandbox. A wide, wide, wide open sandbox. The story is completely stupid, but don't concern yourself with that. It's got plenty of angles - sandbox fans will love exploring the islands, vehicle fans can have a lot of fun with the various planes, helicopters, and boats (cars suck though), and there's no shortage of explosions. And there are over 300 settlements scattered throughout the map, each of which has various items to collect and stuff to destroy, so if you're a completionist, you can go absolutely nuts finding everything.
For JC2 I use a gamepad. You have to change a few things to make the mouse work well - you must turn off VSync and you generally have to reduce the settings slightly. I actually got much quicker loading times and better overall control by simply turning AA and one other setting down slightly - it looks almost as good and it takes about 1/3 as long to fast travel.