I think the HD650 presents things differently, I wouldn't necessarily say one is "better" than the other. They are both on the high end of the mid-fi class (650 rarely sells below $350 and it's MSRP is significantly higher than that). I think the timbre of acoustic guitar as well as vocals excel on the HD650. The THX00 handles electric guitar and electronic music better than the HD650. Both can be pretty well rounded with most genres but I would vote someone into harder rock/edm go the THX00 route and those into accoustic/softer rock, jazz and vocalists go with the HD650. Neither has an expansive soundstage although I think the HD650 has the edge due to being fully open.
Those Fostex are nice. I like my HD650 for classical as long as it is plugged into a good strong high impedance headphone amp. These things sound like drugstore cans if you plug them right into a phone.
But with a good DAP and a beefy amp at rational volume levels, the 650 is just amazing. You can't get better sound for $200, period. Invest in a good headphone amp that is known to play nice with the HD650 and your chamber music, jazz combos, and other direct-to-2-track-master recordings will give you an easygoing "you are there" feel you may never before have gotten from recorded music.
But your big band, electronic, percussive pop and rock are going to need something with just a little more slam. Not that a big amp doesn't give these cans plenty of bass authority. But you can go deeper with more power with other flagship headphones.