Ignore all the juvenile "who would play games on a tablet or iPad?" comments, the best iPad on which to play games is either or both depending on games and what kind of devices you prefer.
The mini overall (in my opinion) is the better of the two for playing games, but for me it's because it's so much easier to hold while you're playing especially if with some of the onscreen controls. With the Air I prefer games that benefit from more physical real estate, games with cards and board games or I've been playing Trexels for weeks on it and appreciating the extra physical space you get on the Air.
I'm quite excited about getting a controller when the right one is released (none yet quite fit the bill) and I'd planned on getting one to wrap around the mini (they pre-announced one that looks interesting), but I'd get a (detached) wireless one for the Air because it just doesn't for me feel like a device that's fun to hold for long periods of time, where the mini is fine to hold no matter what you're doing on it.
Personally (this is my opinion based on owning both devices, neither of which are bad for gaming), with all other things being equal (in how you rate the two devices) if you really would enjoy both of the devices equally but want the one that delivers the better gaming experience, it's the mini, without a doubt.