Many people use monitors with 144hz refresh rates. And increased FPS means you can turn graphics up, or enable more sophisticated anti-aliasing solutions, without impacting absolute performance.
That's true, but also some companies cough Nvidia cough have drivers that aren't up to snuff with an OPEN SOURCE system. It's crazy that the software is FREE to access and really there would be no need to pay any real fees to develop better drivers for systems. AMD is one of the big players that has actually been working with the community to help support their cards.
This is not true: If you increase your target FPS to meet a monitor refresh rate, you must turn down your AA or other graphics settings to compensate when using the same hardware. Going from a 60 Hz to 144 Hz monitor more than doubles the FPS required for Vsync, which requires double the hardware performance to take advantage of the high refresh rate.
If you have 160FPS on a 144hz monitor, you can turn things up. If you have 145FPS on a 144hz monitor, you can't.
That's the only point I was trying to make there.
My point is that the difference isn't going to be enough to be meaningful. If your GPU can drive 144 FPS on your Windows install it can probably drive 144 FPS on your Linux install with the same graphics settings.
I'm just noting why it's not "just a pissing contest". You're right that performance will be similar for games which were built with cross-OS compatibility in mind. But the differences in performance do matter.