Premier = top spec
F-Sport = Sportier spec
F-sport has sportier trim additions and the LFA style gauge cluster, but harder suspension (I don't find mind too bad though, some people exaggerate how bad the ride is).
Premier, commonly has the cream interior (I assume it was the standard option on the premier?) which personally I don't like, but you can get black leather too. They come with the Mark Levinson system (which I am led to believe is very good), blind sport monitoring and some other bits like heated/cooled seats.
You can get F-Sport models with heated cooled seats (which I have) and a upgraded stereo option (Premium Nav (I have this and it's pretty good) or Mark Levinson, ML being hard to find on an F-Sport though). You can spot if it has at least the Premium Nav system by looking at the nav controls near the gear stick, base nav system has a rotary dial, premium + ML have a raised palm rest and a rectangle joystick type set up.
The LFA style gauge cluster is cool but mostly a gimmick.
Cars are exact same horsepower.
It depends what you want from the car really. If you want toys and a comfy ride I'd go for a Premier, or a Luxury with some options.