There are a number of differences.
The major differences is that the F has one less fan, owing to the fact that it doesn't have a G_Sync module. Also, for the same reason, the firmware on the F can be updated.
There is also the worry that the F can not use 10-bit data during transfers for anything above 100Hz ( you can manually configure it for 120Hz but not for 165Hz) but graphics cards have long had a way round this and happily manage to dither by transferring data over two frames. The end result is that in gaming 10-bit and 8-bit data transfers are indistinguishable, so it's not really a very valid worry.
One of the biggest concerns with the F at the moment is that it doesn't seem to work so well with some AMD GPU's whereas there are no reported problems using AMD with the G-Sync version. In fairness to the F, though, it's early days, and even if there is a problem then it may be resolved with a Firmware update.
The F also has additional features, you are best just looking those up to see if there is anything in particular you need.
For me, the only downfall of the monitors is that on darker backgrounds the colour fringing is very noticeable (on both monitors). It's not a problem in games though.