No one can say what sounds better to you. When it comes down to it sound quality doesn't matter as much as enjoyment so it depends what you like. The HD600/650 are headphones designed to have a system built around them and they keep giving when you upgrade your equipment, it's basically a last stop unless you want a different type of sound. When I tested the HD598 to the HD650 for gaming soundstage was similar but the HD598 is a leaner headphone with lower quality drivers. It doesn't separate sounds how I personally like(a bit smeared) but many others find it acceptable. The HD650 is warm, engaging with fantastic mids so voices in games will sound full and fleshed out. I liked using them for games like the Witcher which have a great soundtrack.
Your budget is limited so the best you are looking at are
HD650/HD600(£200-250) - Warm, bassy, natural and engaging and resolving.
K712(£212)Warm, extended well at both ends, resolving with a good soundstage.
K612(£90-100) balanced, fairly resolving for it's price, good bass extension and good air