Well if price isnt an option then the iMac is a better machine. It obviously comes with a screen/speakers, and has better specs than the Mac Mini (better processor, more RAM than the base Mac Mini, and a better graphics card).
Ofcourse, it is more expensive, but you did say that money wasn't a factor so...Why not the iMac? I personally have an iMac/MBA set up, and I have to say that its great; MBA for when I'm on the move, and my iMac for when I'm at my house.
Something you could also consider is buying a Thunderbolt Display (or any other type of external display) for your MacBook Air instead.