I agree about HD650 being more "refined" and by that I mean smoother and more colored at the top end. Which one of these two we perceive as more detailed (whatever it is meant by that) can depend a little bit upon our hearing sensitivity, our gear etc. Personally I perceive HD600 as more tonally accurate and revealing of the true timbre of instruments for example. They also have the ability to let me be focused on music during listening sessions for much longer than HD650.
In direct comparison with HD650, HD600 can be perceived as a tiny little bit more "congested" and less "easy going" with more complex music. With small orchestras - chamber or jazz - HD600 is as open and dynamic as HD650. Personally I love them both and think they have similar "fidelity". I don't see any of them as the other one's upgrade.
I chose HD600 because I see it as a perfect complement to my HE-500. HE-500 is another story. It is richer, with much more going on in the sound than with both HD600 and HD650, better dynamics, faster transient reproduction, better textured low end etc. HE-500 is not as natural as HD600.