As extrabigmehdi said, the HD650s are darker, with less of a treble emphasis. They are less fatiguing to me, so I can listen for longer, which is a definite positive. They sound thicker, warmer, and more laidback, with a bit bigger soundstage.
The 940s, on the other hand, have more detail, air, sparkle, speed, and energy. And isolation -- the HD650 is an open headphone, so if there's any noise around, the 940 is better.
Overall, I prefer the HD650s. I like my music on the warm side, but I also like a change sometimes. For some music, the 940s just sound better (e.g. female vocals, acoustic, any music where the treble is more important than the bass).
I think your choice of DAC and amp depend in large part on your sound preference. The 940s and HD650s are opposites in many ways, and you might want to tame their particular sound or not.