Never heard the Game Zero. I own both the 598s and the 600s. The HD 600s are on another level. There is bass although I'd still consider them bass lite and the 600s have a smaller soundstage than the 598s. The soundstage is the only place the 598s beat the 600s though. The 600s are quite intimate.
I LOVE my 600s. But not with everything. If you have a bad recording or low quality source then the 600s are not forgiving at all. They also wouldn't be my first choice for newer pop/hip hop or EDM.
HD 650s are more forgiving. They also have more bass presence, a slightly larger soundstage and a warm tint. The 600s are more neutral, more resolving and more intimate. Both the 600 and the 650 do that magic thing with vocals especially female...