It may be the same chip; Intel Core i7-2635QM 2.0 GHz although this has not been verified that I can find. If this be the case, then it would be down to ssd or sATA version. Or price. The mini wins if this the case..
the 2011 mac min definitely wins! it was reported that the 2011 macbook air (with ULV chips) compare with last year's top of the line 17"MBP, so of course a normal voltage processor would beat it. even the 2.3GHZ i5.