Hello there,
My recommendation is for Battlefield, which is what l usually play (B3 and B4).
From the HPs l have tried, should you want an open-back model, l would go for the X1s (already recommended to you). l especially value on them their comfort, bass impact/quantity and soundstage. They're pretty good also for movies. These would fall into the 'immersive' category. l still have to hear anything more 'immersive' (in that it sounds so real) and cool than the X1s reproducing the sound of the ACE 53 SV mounting the LS06 suppressor, in B4. Cable is replaceable (so you can pick the length you need), however not the earpads. No need for an amplifier with these (unless you like to listen very loud).
lf you want a close-can, then l would pick the Beyers DT-770 (l have the 250 ohms version). They also do well in movies (if only sometimes dialogues can seem a bit distant). For gaming, they're a great balance between competitive and immersive, as they have good bass (good sub bass, not punchy, though), great highs (to hear shots and footsteps) and pretty good soundstage (l would say you pinpoint enemies easier with this than with the X1s). Cable is non-changeable, and not too long (take it into account if you will be plugging them to the back of your PC or console, and these are not close to you). Comfort wise... well, l will never forget someone (l think in an amazon review) saying that they feel like "having a lamb over your head"
(maybe someone should create a smiley to use in these occasions
). They're super comfortable; besides, ear pads are replaceable. You might need an amplifier (back in the days, l used them with a Xonar DX -no amp- without problems).
lf l had to pick only one, l would be in trouble. l guess, l would go for the close ones, as they are more polyvalent (on the go, with someone in the same room, etc.).
Finally, if you don't have much experience with HPs, amps and DACs, l would NEVER recommend you buying anything too expensive (more than $500). l would suggest you to buy these 2, for example, instead of one single HP that cost the same as the pair. Why? Because IMO, getting to know different HPs will help you grow and determine your preferences. Besides, you could have 2 different HPs, for different uses and, also, as they say: "in variety is the taste".
Let us know of your buy!