They're both great tablets, and it's a matter of personal preference and usage which is right for each person. If you can, go to a store where you can handle the demo models, and see how they feel side by side. Sometimes one of them will just feel right.
Do you typically wear a jacket or carry a purse? Most jacket pockets are big enough to carry the mini. That's a big part of why I like the mini so much, as I don't even need to have a bag or a briefcase in order for it to always be close at hand. But if you don't wear a jacket or carry a purse, the difference is much less significant; a backpack or briefcase will carry both of them about equally well.
When you read something, do you typically hold it closer to your face or further away? If the latter, you might prefer the Air; if the former, you might prefer the mini. I'm a bit nearsighted myself and tend to hold things close; that might be part of the reason I like the mini.
Do you want something that goes absolutely everywhere with you? Or are you content with using a smart phone for those times you need something completely portable?
Do you want to use it for reading sheet music? A few people have commented the Air screen is much better for that.
Do you mind needing to enlarge the text a bit when viewing websites, or viewing them in portrait mode? If that bothers you, the Air might be better. On the other hand,it bothers me a little, but for me the portability of the mini is worth it.
Do you want to watch movies on it? I tend to think movies look better on a larger screen, though a few people have said they like watching movies on the mini on the couch or in bed.
I find thumb-typing easier on the smaller screen of the mini. On the other hand, if you're going to want a physical keyboard accompanying your Ipad, then the Air is an obvious choice.