I agree the HD650 has much better bass - there's much more of it and therefore you really feel it. I think the DT880 bass is more precise/distinct, but less. Overall it feels like the HD650 bass goes lower (but not sure how much of that is due to quantity). The mids on HD650 are fuller and smoother. The treble is very much there on the 650's, but not at all overly prominent. I would say it's got a great balanced sound, though on some recordings that midbass boost could be a bit much if you're sensitive to bass.
I'd say the DT880's have balanced/neutral mids and bass, but more prominent treble - so some differences in our assessment there.
I did fairly extensive listening (coincidentally) last night with both cans on both my Crack w/Speedball and EF-5.
The EF-5/DT880 combo was what I would say is the closest/most convincing to making me feel like I'm right there, live. Everything is so distinct, sounds are separated and airy.
The EF-5/HD650 sounds great, but more like a beautifully produced recording (vs live). Everything is blended together (which is pleasant, though less airy).
The Crack adds more smoothness and warmth to both cans. Overall, I prefer it by a bit to the EF-5.
Between the DT880 and HD650 on the Crack, it's mostly mood/recording dependent, but in most cases I'd go with the HD650. Nothing sounds bad with the HD650. I listened to some metal (well, what I'd call metal - Nirvana for example) and it sounded great. The DT880 can sound overly bright (especially coming straight from the HD650) on some recordings - while going from the DT880 to HD650 doesn't give me the impression of dullness ever (at least on these two amps).
The DT880 is brighter, faster, and I think more detailed on the high end due to the higher quantity of treble. So overall, I agree with some small differences, except to say the HD650 treble detail and quality is better than DT880.