As far as I know, if performance is your concern, nowadays you're not making an automatic mistake for going with ATI on Linux. I've personally only used NVidia (well, and 3dfx) and never ran into problems caused by the closed-sourceness of their drivers. Even though I was running old hardware and the often cited theoretical danger of closed source drivers is WHAT IF THE MANUFACTURER DECIDES TO DROP SUPPORT FOR YOUR CARD? That said, I'm considering switching to ATI the next time around for two reasons: a) Their sort of false advertising of the 970 with its crippled 500 MB memory block (haven't seen any practical problems yet, mind) and b) The fact that my current laptop's CPU died
an engineering failure heat death (resurrected it as a zombie, expecting it to completely stop working in a month or three).
I haven't actually got any experience with proper gaming laptops. I always just shopped with the desire to maybe play the one or other older or less demanding game. Proper gaming laptops are just not worth it, I prefer having a proper tower where I can switch out the GPU after two or three years for the real gaming. For my personal purposes, the Intel integrated GPUs of Skylake CPUs would suffice performance wise. It's just a shame that their drivers are crash happy.
Oh, and funded with about two hours left on the clock. Phew.