The advantage would be you'd have a Naked Lady engraved on your horn....and an underslung double-socket neck....and 6M's are 'cooler' than 14M's.
From a sound and blowing standpoint, there would be no difference (or rather the difference would be no more significant than the diff between one 6M and another, or one 14M and another). Conn, unlike other mfr's like King or Martin, did NOT roll 2 different body and necktube designs for their upper and second shelf models off of their assembly line. So neck tube, body tube, bow, bellpieces were the same (except for the RTH). Therefore, they blow and sound the same....
The keywork is a bit different, particularly the side keys and the pinky table; shape of a few touches, obviously a different octave mechanism, and the way the front F is mounted. The 6M generally does NOT suffer from the ergo issues the 10M presents to some players, probably solely because of its scale.
However, personally.....I don't think a 6M layout is any 'slicker' or more responsive than the 14M mechanics. I think what may happen here is you'd end up with a sax which is more similar than different from what you already have, from a playing performance perspective.
One can argue (and for kicks, I will - sure) that you could use that $ and 'spread your wings' a bit and perhaps try a Martin or King or Buescher instead....because there you would likely end up with a horn which is 'more different' from/to your current Conn.
Just a thought....
Of course if you have the $ and wanna see for yourself, grab a 6M.
They hold their market value pretty well so you wouldn't likely lose much if you decided to resell it.
It'd be interesting to hear whether you found differences as far as playing performance to be substantial.