Best vid I've seen on the subject. It's nearly 20 minutes but the guy examined tearing with a 1200FPS camera and also measured button-to-pixel delay for input lag. The TL;DR is that without an fps limiter, there is tearing even if your eyes don't notice it much. And the greatest input lag is with Vsync also enabled. The best combo is Gsync/Freesync ON + in-game fps limiter (2 below max Refresh Rate in most cases, not always). And if a game doesn't have one then Afterburner/Rivatuner fps limiter.
But for the stutter you're experiencing you should also experiment with your mouse's polling rate. You may need to decrease or increase it for the new screen. I had something like you describe when I picked up a Logitech G300S. In my case, the default polling rate (1000Hz) was too high for my 72Hz screen. Lowering it (to 125 or 250 I think, have uninstalled the software since and just kept onboard profile saved) immediately fixed it.
