G-sync monitors have nvidia chips in them that remove the need for V-sync. So you'll get no screen tearing, which can be a real pain sometimes.
Prime examples are Shadow of Mordor. Game shipped with terrible frame sync and a v-sync option in the settings that caused random frame rate drops into the 20's. So I had to force it with D3D overider and place the game in "borderless window" mode. I've had v-sync issues with a fair few games so I can see why these G-sync monitors would be a good idea.

Lower response time does help prevent "ghosting" etc. If you go for a 60hz monitor 5ms is fine. If you go for a 120-144hz you want 2ms or less.