It's difficult to say what causes stutters in most cases, could be Windows, drivers or game itself. The list of things to try can be extensive but i guess need to try them all.
I've been using a Gsync monitor for couple years now and very pleased with it. It's an Acer XB270HU and first for me as well going from 60 to 144Hz. Gsync's main goal is to eliminate tearing, use of Vsync, avoid input lag and improve motion with variable frame rates as you're aware.
It's all up to the game's optimisation and how it uses the system and also how Windows behaves in the background.
Games i've played that are generally smooth but not always as with 3Dmark and source games. Those games are Farcry 4, 5 and Primal, Ghost Recon, GTA5, Dying Light. They are generally smooth but how things are loaded in and out of ram, Vram and HDD/SSD, there can be quite a bit going on so i just accept that some games aren't going to be 100% smooth all the time, depends how they've been developed and optimised for PC. Just my experience with games. I know my system is lean and running well for it's age. 2600k 4.5, 16GB ram, 1080Ti and SSD, Win7.
Depends on your issue how bad the stutters are could be the result of Windows settings, drivers, or game/game settings.
We'll go through some of the usual rounds of troubleshooting and suggestions for you to try.
First though, run 3Dmark firestrike or timespy and see if you get any stutters. Basic edition download bottom of page.
https://benchmarks.ul.com/3dmark
What games have you tried that stutters in? Can you try Halflife 2, Left 4 dead or Portal?
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Things to try: Assuming you're on Win10 with that system?
Windows and Nvidia power plans are set for performance.
Make sure game bar and xbox dvr has been turned off. Xbox dvr (on by default) recording app records your game play automatically. Another feature of game bar is fullscreen optimisation which is like windowed borderless fullscreen. Can mess with some games and the option for it can be found under the compatibility tab of the game's exe or shortcut.
Run malware/virus scans. Since you're running at a higher frame rate now you need as much cpu power as you can get. 60Hz might not have been as noticeable so make sure the cpu is sitting at or near idle usage before playing games.
Turn off share Windows updates to strangers. Shouldn't be an issue but i'd turn that off anyway.
Reinstall gpu drivers by using display driver uninstaller first in safemode. https://www.wagnardsoft.com/
Install Chipset drivers for your motherboard if haven't from the vendor's website.
Last for now, don't let Geforce Experience optimise your games, usually gets it wrong and set things too high or use of Nvidia's gamework features that can be buggy in games that use it. Since using 1440p resolution, might find don't really need antialiasing anymore either and squeeze more performance.