Rhythm Man and I like these threads on guitar chords.

One of the main differences in your choices of how to play the F chord is your music style, like Jande said.

The following is advise from Rhythm Man:

The way to play an F depends on the song you are playing. If you want to have an open, ringing sound (like you want in most country music)then you need open strings and you can capo in 1st fret, play in E or Capo 3rd fret, play in D or Capo 5th fret, play in C. All these are F chords.

If you barre an F or wrap the thumb, this is great for Texas swing style, blues, and up-tempo country music that calls for closed chord positions.

A good rhythm player must know when to use what position of the chord he needs.

Gotta Go.

Glenda & Bob