G-sync and Free-Sync solve the same problem in two different ways and are not cross compatible. The problem is when your GPU is unable to produce enough frames for every monitor refresh cycle. This leads to screen tearing. They solve it by giving the GPU control of the monitors refresh rate. V-sync, Adaptive V-sync solve it in the opposite manner, the GPU will not begin drawing a frame until the start of a refresh cycle. If a frame isn't available, it draws the old frame again. Effectively this leads to an increase in latency since you may be seeing an old image. V-sync and Adaptive V-Sync will also limit the frame rate the GPU produces to whatever the monitor's refresh rate is. G-sync and Free-sync can be set to ignore synching above the monitor's refresh rate.
Stuttering, is more a symptom of some component in the system not being fast enough for the given settings. IE a slow drive, not enough system memory, not enough video memory, not enough cpu performance. Check your temperatures, throttling can certainly lead to stuttering. Lower your graphics settings to see if the problem continues, likely the rest of the computer then. Always check your running software, might have something spiking the CPU, like a virus or malware.