I don't have a strict preference - it's dependant on the game and the mood I'm in.
AES is preferable for a casual blast; I can quickly pull out the console and sit on the floor/couch and still use a decent controller (the stick of course). For this purpose, although I don't own either one, I don't see a CMVS or Supergun any different what-so-ever.
MVS is preferable for a serious attempt at a high score, or a competitive one-on-one in a bar, arcade or games room set-up. As Joe8 said, you can get into it more and it's a more authentic arcade experience.
As far as
collecting goes, I'm most interested in the AES. The main reason I have an NGCD is to burn games to play on real hardware, most importantly homebrew stuff I'm working on.
@Joe8 - you also forgot NeoGeo-X!