I've always heard the 600's referred to as more "neutral" than the 650's. I can't personally hear too much difference between the two, with the exception of the 600's having a higher top-end. The major complaint of the 600's is that they are not bassy enough. For me, it's about perfect. I listen to a huge amount of jazz, and the snare stands out perfectly without any bassy bloating on the 600's. I'm able to hear every nuance and difference in the way the drums are hit.
One of the songs I use when testing out headphones/amps/dacs is "My Favorite Things" by John Coltrane. There is so much going on "in the background" with the snare and piano. This gives me a good idea of the capabilities for the equipment I'm testing.