I've run carpet, no carpet, Bedtred, and Line-X Premium. From reading this thread, I think my opinion goes against some of the others, but I would like to give it. Take it or leave it as your situation has to be different than mine since you are not me.
Carpet
Pros:
Nice looking
Hides wiring
Good sound insulation
Good temperature insulation
Comes with Jeep so cost effective
Cons
Difficult to get mud and water out
Stinks when wet for a while
Mildew issues from water
Difficult to get to drain plugs
No Carpet
Pros:
Easy to clean
Easy to get to drain plugs
Doesn't hold water
Doesn't stink
Free to remove
Cons:
Poor sound insulation
Poor heat insulation
Doesn't hide wiring
Scratches fairly easily and can lead to rust
Floor mats slide around
Bedtred
Pros:
Looks good
Hides wiring
Good sound insulation
Good heat insulation
Waterproof
Cons:
Traps water on top and underneath
Difficult to get to drain plugs
Water underneath can stink
May have to remove to clean thoroughly and then reinstall
Somewhat expensive
Line-X Premium
Pros:
Looks good
Good sound insulation
Good heat insulation
Waterproof
Easy to get to drain plugs
Doesn't scratch
Doesn't fade
Easy to clean
Cons:
Doesn't hide wiring
Permanent
Expensive
If floor mats are used they slide around
My opinion:
Since I live in KY where we have lots of weather that provides us everything from hot and dry, to hot and wet, to cold and wet, to cold and dry, I prefer the Line-X Premium. The reasons are that I don't have to deal with getting water underneath it like carpet or Bedtred and it smelling awful, or having to remove it because of water sitting on top of it. Another reason is when wheeling here, you get mud inside. The only other option that I've tried that is as easy to clean up the mud is running nothing. The carpet was a mess, and I had to remove the Bedtred, pressure wash it, let it dry, and then reinstall it. As long as I have the drain plugs in and my Mopar slush mats, the sound and heat with the Line-X are very similar to the carpet or Bedtred options. The mats do slide around a little, but it isn't very bad since the Line-X has a texture making it an acceptable compromise for me. The Line-X doesn't hide the wiring, but I put it into some split loom, so it doesn't look bad. It's another acceptable compromise for me.