Exactly what robonb said. There is absolutely no difference. I was using an iPad two with no issues. But I upgraded to iPad Air 2 wifi+4g LTE, wow is all I can say way way way better. The slightly bigger screen and anti reflective screen also brighter make a huge difference.
You should not notice a difference since they both have an A7 processor. If you want to get the best performance, then get a device with an A8 processor. The iPad Mini 2 works just fine for me though, so an A8 processor is not really necessary.
The Air 2 is obviously very very good but as I only use it for the Phantom just a bit too much to spend. As for there being no difference between the mini 3 and mini 2 apart from the touch id I shall get a mini 2. My present Galaxy Tab 3 gives such a lag with the pictures as to be useless, First time with an IOS device and a Phantom hitherto I always used Android.