The Beyerdynamic DT990s will give you a bigger soundstage with more "3D" sounding spatial cues and some extra bass will add to the immersion too. Any version of those will probably benefit from an amp though.
The D2000s aren't as "3D" as the Beyers but they have plenty of bass, go deeper than the DT990 or HD650 and should be fine from your mixamp.
I found both of those to be have pretty fatiguing treble but many other people aren't bothered by it at all so it depends on your preferences.
The HD650s are smooth, detailed, and relaxed. IMO they don't really excel at anything but they don't do anything badly because they don't have any glaring weakness either. I think that they're more of an all-rounder.
The D2000 or DT990 will likely pull you into the game or movie a bit more than the HD650 and games and movies will probably mask the D2000's and DT990's weaknesses (to those people who think the treble is a weakness anyway) since in games in movies the focus isn't always on the music.
Thanks for the great feedback. Sounds like there's pros and cons with all the headphones I'm looking at! It's a good job half the fun of buying anything audio-visual is the research :-)