I compared them both via the very delicate DAC/Amp D100 MKII. I personally own the X1, while my brother owns my HD650; which I sold to him.
I haven't owned the X1 for so long, so the burn-in time does not exactly match that of the HD650; that's why I haven't gone into any serious reviewing of the headphones, but I can give some initial impressions. The burn-in period on the X1 is somewhere between 25h and 30h.
The difference that I discerned was this: Both are what I would identify as warm headphones, only the X1 seems more open, and has more clarity than the HD650. In comparison, the HD650 seems to have denser and thicker mids, it renders vocals more forward and heftier than on the X1, but then again, it almost sounds muffled depending on the track. And on the X1, the vocals, again depending on the source/track, can make vocals bear more space - give them more of that clearness and airiness. I mean, separation is great on both headphones, but the X1 seems to bolster additional soundstage and overall feels more open than the more congested HD650. This could partly be due to the midrange on the headphones; but I can't really say as I haven't seen the FR on the X1 yet - I'm only going by what I hear.
Mid bass is quite similar, only the X1 has more sub bass; which in turns gives more body to drums in some pop songs, but especially distinguishable when listening to electronic music that has a lot of sub bass dips.
The X1 has more treble energy, but I almost felt as if its treble was almost smoother even though the HD650 has less treble emphasis. Only noticed it on very few tracks.
Overall I feel that both headphones are stellar for their price range. They have some similarities, but still quite distinguishable. The X1 is far from being a bass beast like the DT770, but it might as well take the lead from DT990 in open design; and the X1 is not exactly a K701, but it feels like it's somewhere in between the Beyers and the AKG, to me - which is great. The HD650 is a bit more forgiving headphone, its thicker and more rounded in character, and is less engaging than the X1. Nonetheless I feel the HD650 is a good fit for certain types of genres, most preferably vocals; while, to me, the X1 fits almost any genre. But, after all, it all depends on personal preference.