I've been GS for several years. The biggest perks I have seen are: (1) better upgrade opportunities and can request them either 4 or 5 days in advance if you are not yet upgraded, (2) dedicated line and they will move all kinds of things around for you including pushing through upgrades for you and travel companions, (3) they will hold a plane for you if you are connecting and have a car drive you across the tarmac from one gate to another if a tight connection, (4) if your flight is canceled due to weather, you will get rescheduled and prioritized on the next flight and they will pay for a hotel for you with food, etc. (yes, for weather), (5) a travel companion with your same perks. There are others but these I have found valuable. Not sure what overlaps with 1K.
Enjoy your GS status!
ETA - in hub airports you get a special check in location that moves to the front of the line at TSA