I own both and I think the 650's are just the better all rounder IMO. I guess it's kind of a boring qualification but that's not the case at all. It encompasses quite a lot of things.
The greatest asset of the 600's is the incredibly natural sound. It's really something special and the 650 doesn't quite have that, but in return, it has a very enjoyable, smooth and polished sound with great treble that invites you to listen for hours on end. The 650 is less fatiguing than the 600's; the 600's aren't necessarily fatiguing but I find every so often that their treble is stronger than I like.
The 650's have a more neutral sound - everything, from bass up to treble, sounds integrated and uniform. The only exception is the subbass, which I guess could be considered the 6x0's only (pseudo)weakness. On the 600, I sometimes feel the midbass is just a little less than I'd like (though by no means weak) and the treble seems to stand out just a tiny bit for me. Very, very, rarely do I experience issues like that with the 650. I always enjoy the rich mids, I always appreciate the bass and the treble is never too much or too little.
The reason I call the 650's the better all rounder is because eventually, I always end up going back to them. I might periodically use the 600 because I love the natural sound. But ultimately, the 650's (to my ears) perfect frequency response always wins me over.
Ofcourse, this is all assuming an amp that doesn't mismatch impedance and has little to no deviations on its frequency response (+/- 1 db). I could easily see a speaker amp providing the 650's with an unwanted mid-bass hump.