Practically everyone that used the HD6xx line complains about the size of the soundstage being imaged, Overwatch included. I don't mind it for the games I play since I use it more for immersion than to pinpoint sound sources, but if I've seen that kind of feedback I'd note it. For music you can definitely do much worse - only the soundstage size is the problem but otherwise the location of each instrument is proportional enough to each other.
That said, even if you don't care too much about the soundstage, the problem is that many people find the HD650/6XX/660S too dark. If you specified that you were looking for something warm then no problem. But if you're looking for a good deal of treble your initial impression of them might not be good. The treble curve is relatively smooth, and so is the bass curve, the thing is it's much stronger below 1000hz than above it. So while the treble is smooth the problem is that that imbalance makes people focus too much on how much stronger the bass is and think there's no treble.
My HD600 is EQ-d and using angled earpads that apart from moving the cymbals closer to the center together make for a sound that's closer to the HD650, ie, its 3500hz peak flattened and everything below 50hz brought up a bit more. Since pop music, and particularly K-Pop, can be recorded quite hot (and I'm not talking about T-Ara's dancing), not making the treble any brighter is a good thing. No way to tell if that will be great for you.
That won't be a problem on the HD800 though. If you can get it for the same price as the HD660S, then it might be a good buy. Just note that that won't necessarily be a bargain for long - earpads for the HD800 cost $90 per pair. The HD6xx series' costs $60 but there quality alternatives like the Brainwavz HM5 pads will fit on the mounting bracket of the original Sennheiser pads, and they cost $20 to $25. At least take that into account, especially if the reason for the low price is that they're worn out. Cable replacements aren't cheap either, because unlike the HD6xx and HD25 series that use proprietary Sennheiser plugs, there are at least a lot more of them out there to make the cable prices affordable.
If anything though they'd be a lot less finicky about amplification than the K701. Although personally even at that price I'd be more inclined to get the K702 (HD600 or Massdrop X Sennheiser HD58X if you really don't care about soundstage), although the AKG earpads cost the same.
