ANC is anti noise cancelling.
I typically go to Whathifi.com, read reviews and see which audio products sound like they would work for me.
I recently upgraded from a Momentum 2.0 over ear headphone to a Sony XM5. I prefer the Momentum audio profile, it's easier to listen to for extended periods and I prefer the sound stage and the warmth and musicality that it adds to the music. The XM5 is technically superior and I do like it, I just find that it can be less comfortable for extended periods.
I therefor use my Sony's in the office/commute and game with my Momentums since I have an Ifi Zen 2 DAC connected to my PC. I play PUBG with the latter combo and it's amazing - I can hear very distant sounds that other teammates miss (a car drives by at distance).
If I had £200 to spend on a new headset, I would probably get the
Grado SR325x
Reading a review of your DAC, I can't say I'd like the sound it produces given the comment of "It’s not entirely warm sounding, but it’s also not too cold and sterile like you’d get with something like a Magni 3".
I have read the review of your DT770 headphones
here and I think that you might see an improvement for a better DAC rather than a new set of headphones. I can see that they aren't the perfect set of headphones. I'd
try a better DAC first before just buying a new pair of headphones - do you know someone with a very good DAC to lend you for a days gaming?
I can't really say definitely upgrade to the DT 990 PRO as the comment of "The Beyerdynamic DT 990 PRO are slightly better critical listening headphones than the Beyerdynamic DT 770 PRO thanks to their open-back design. Both headphones are similarly built and are comfortable. They are practically the same headphones, but the 990 are open and the 770 are closed-backs."
Why would you buy, essentially, the same set of headphones?