Well, NVIDIA's marketing says the advantage of getting a G-Sync monitor amounts to basically better QA. And a casual search on the internet tells me people tend to get a better experience with a GSync monitor over a FreeSync one. The thing to note is FreeSync is cheap to slap on a monitor. That does not mean that any FreeSync monitor will provide a decent experience. In other words, a $150 FreeSync monitor is likely to be "meh" in terms of features than a $800 FreeSync Premium monitor.
As far as I can tell, though my experience is limited, a FreeSync Premium monitor seems to have no real discernible difference to a regular GSync monitor.