The monitor refresh rate is associated to mouse curser aka cross hair.
So, add game software latency to that refresh figure. It isn't a 200/60 difference anymore. It's perhaps a few percent. Or not at all if the game engine incorporates timing to keep game playing equalized.
Anecdote: Back in "the old days", a display card manufacturer came out with a cutting edge 60 Hz card in a world of 45 Hz hardware. Game players were elated. "It's so much better. No more headaches due to flicker. Etc." Except that it was discovered that the display driver configuration panel loaded the same parameters for 45 Hz and 60 Hz. Discovered, I think, by people configuring Linux X11 displays with hand-edited XF86Config files. Suddenly, the gaming BBSs were full of people complaining of the same headaches. Pretty much the same as the guy who "cured" an office co-workers WiFi sensitivity by covering the flashing lights on the router. And, "My guitar amp goes to eleven."
You are faster because the display driver box says 200 Hz.