Rather than try to write a long review of each phone (which has been done many times) I'm going to just write a few observations about the strengths and differences between the two. As in all such instance, YMMV, IMHO etc. etc.
In terms of ease to drive, the HD650 is easier...although improvements in source and amplification do raise its' level of performance quite a bit. It's not just about loudness, but clarity, impact and tonality. I used four amps in this comparison...although most comments are restricted to just two of them. The amps are a Headroom Supreme (about 1995 vintage), an ASL tube amp that has outputs both for transformer coupled and OTL. It has a pair of EL-84's for the output and a vintage windmill-getter 5751 as the driver. I also used my Pioneer SX-1250 and Marantz PM11-S1 integrated.
The 650's are a warmer, more romantic sounding phone. There is a midbass/midrange bump followed by a gradual roll-off that gives them a lush, darker sound and the impression (not fully accurate) that the treble is lacking. Actually, the lower treble is down a bit, but the high end is not.
The 500's are more neutral sounding, plus have the unique planar sound that you either love or you don't. It goes deeper in the bass and has more apparent treble than the 650. It is also harder to drive. One example would be that the Headroom Supreme has enough power to get quite loud, but the tautness in the bass is not there like it is with the Marantz or Pioneer amps.
Both sets of cans have a warmer sound with the ASL tube amp. It lacks the grip in the bass that the solid state amps have, but the midrange is just lovely. It brings the midrange forward a bit with the HE-500's.
The 650 is a more forgiving phone than the 500. I listen to quite of bit of 60's/early 70's rock and a fair amount of that material is not recorded particularly well. The 650 has a bit less emphasis on sibilants or harsh horns.
With that said, the impression of detail is more apparent on the 500's. It is not detailed as in overly bright/analytical (although it can get close to that on the wrong material) it simply tells you more about what is going on in the recording. On "Sinkin' Soon" by Norah Jones, there are a number of instruments both stringed and percussive that are in the background that I never noticed with the 650's. To be fair, once I knew they were there...I could pick them out of the mix with the 650's as well...but it was with the 500's that I first heard them.
The soundstage width for both phones is, to me, similar...but the 650 has better depth. You get a better sense of acoustic space with them. The 500's on the other hand gives you a clearer sense of when the reverb is because of the space or is electronically induced. They also help you pick out more individual voices in group recordings such as "Psalms" by the Turtle Creek Chorale. The same songs on the 650 sound great, but are a bit more "of a piece" than a group of voices that you hear individuals in.
The bass is a bit more punchy on the 650's and the cans do sound a bit more dynamic. OTOH, I love the tonality of the 500's and the ability to hear the organ well as it descends the scale in Symphony #3 for Orchestra and Organ by Saint Saens.
At the end of the day, it's hard to say which one is "best". The 500 is more accurate and extended. The 650 is a bit more "fun" and forgiving. The 500 is much heavier and the pads are firmer making the 650's more comfortable (to me). I can wear either for hours, although I confess to doing a lot of my listening in a recliner.
So there you are. The 500's are one of the new darlings and the 650 is a seasoned veteran. Both have their fan boys and their detractors for a reason. I'm just happy I am fortunate to have both.
Hibuck....