If gaming is your primary motive, I'd seriously recommend the mini. I have a nexus 7 and a One X as well but neither can game as well as the mini. Why?
1. iOS has a much better library of games. In addition to that, you often have popular games going for free. I recently downloaded Asphalt 7 and Granny smith for free.
2. The GPU is much better for its resolution on the mini as compared to the nexus or one x. This means that games mostly run with full effects activated and push out good frames.
3. I'd suggest mini over touch because the touch has to push out more pixels than the mini with a lower clocked gpu. Also, I don't know if this point holds much significance or not but the only other ios device with the same resolution as touch is the iPhone 5 which has a MUCH better gpu and devs would likely make their games to run on that hence making them lag on touch. I saw a few videos in which most wanted dropped some frames at some instances on the touch. This point is not valid for the mini because the ipad 2 which still sells has the same resolution and gpu.
If you want to buy a phone for gaming in this range I'd suggest either Nexus 4 or Xperia SP. Both would be excellent for gaming. Coming from a 11 month old One X user.
