I've got HD580s which, for the purposes of this discussion, are the same as HD600s. My portable amps, which roughly equate to the bithead, are only very slightly better then the HP jack on my computer. To get the HD600s to show their full quality you will probably need a desktop amp. A very good portable might do it, but I don't know.
My experiences with both the hd600 and the 650 is that many of the little portable amps don't really do a great job driving them. They work but they don't have the fullness/richness and basic clout that a decent amplifier produces from them.
I have quite a few portable amps and I don't really like to use them with the 600 or 650. One that drives them better is a Xenos amp that I have. (I think it's a Xenos 3 and is large) It only gives about 7 hours of power from 4 AA's but it does actually push the Senns. However, it doesn't have the sound of a quality home amp imo. It's ok and that's about it. It delivers a lot of power though.
The Bithead works but it hasn't got the clout of bigger amps. (Same with the pocket amp and the Move and the Go-Vibes) They all boost the volume, but the quality just isn't there for headphones that need clout behind them. The Senns really do reveal what is driving them.
Also, the louder you go with these little amps, the worse it gets. The sound becomes muddled and compressed sounding. When the batteries start to go, they start distorting on peaks as well and it starts to sound quite nasty.
I would love to try something like a Hornet with them since I have heard good things, but I don't want to spend that sort of money on something I really don't know.
I just think that Senn 600 and 650 and portable are a poor deal although there are people who enjoy them this way. Not for me though.