In the context of gaming none of these - HD6 series is great for a lot of reasons, but notorious for having very intimate and close soundstage.

HD800 is the king of soundstage and imaging, but if thats not in your budget you're looking at one of the AKGs or a Hifiman Edition XS (great soundstage width, height not so much).

Since you are coming from 560 which is super easy to power I will add this: I have only auditioned the AKGs at a shop, never owned one so i can't comment about if a dac/amp is required, but bear in mind the XS absolutely requires a dedicated amp regardless of whatever anyone will try and tell you, without an amp it WILL sound very congested and that is if it even gets to happy listening volumes, so please bear in mind if you are on a strict budget.