The biggest in my eyes is the iPad Air’s wider gamut display with full sRGB coverage. The mini’s Retina Display is good, the Air’s is just better. There’s also more thermal headroom on the iPad Air, which can come in handy if you’re doing compute intensive work on it. If neither of those things matters to you, then the decision becomes one of usage model and portability. I believe the iPad Air does a better job of approximating a primary computing device, particularly in its ability to give you a reasonable sized virtual keyboard to work on. The iPad mini on the other hand is substantially more portable. Although the iPad Air is light enough to come along with me more than any prior iPad, the mini’s form factor makes it even more likely that’ll I’ll bring it with me (the best tablet is the one you have with you?).
In spite of my snark, I do agree with readers who pointed out that, for professionals who rely on the iPad and demand color accuracy, having the best display is important. I don't think that average users will notice any issues with the mini's (amazing) Retina display, but if you're looking for hard facts and numbers, AnandTech's review is the one to read.