The graphic driver situation is abysmal for both. With Linux, you might as well not even bother with modern AMD cards. They've done a terrible job the last few years, often eschewing such things as a change log that shows what this random update you're downloading does.
NVIDIA is much better on Linux overall, but even they have got a lot of limitations and quirks. Performance is much better than AMD, as long as you don't use the open source drivers.
On Mac, the drivers are crazy out of date and seem to be very tied to specific Mac OS releases. I don't know whether to be irate with Apple or NVIDIA/AMD. Linux benchmarks better on many games than Mac OS. Phoronix runs these periodically if you wanted to see some numbers.