My HD650s sound outstanding w/Jazz recordings (I was listening to Art Blakey - A Night In Tunisia, last night...so fun and addictive). Funny thing that Gunting mentions that very set of recordings, below. I think it takes a min to get passed the flaws in the recording, but once you really start listening, it's really got a great overall "feel" to it and actually is quite a nice live sound. I also like Chet Baker's "Baby Breeze", as a specific example (the non-vocal tracks, specifically - the impact and tone on the HD650s are just crazy good - sweet flugelhorn and driving drums, very intimate but so cohesive).
I did have a set of K701s, which when set to the right Jazz CD, really did sound great (in a bit of a different way - really more of an airy sound...great layering/instrument separation). I actually almost kept them, but couldn't get over some fit/comfort and amp/headphone synergy issues. I have absolutely no regrets though, w/the HD650s, they have really come into their own.
I think it's what will work best w/your other components (and what you like). The HD650s really let the great tone of brass and kicking drums (especially) in Jazz recordings shine through, IMO (and no boomy or muddy bass w/the right setup). Even the recordings that are less than perfect...