It depends on the opening. Playing f4 allows Black to play moves like ...Bc5 to keep you from castling King-side. c4 means you can't defend a d4 pawn in the center with the c-pawn.
On the other hand, the Bishop's Opening and Vienna Game both avoid an early Nf3 for they can play the f-P to f4 before Nf3, aiming at a King-side attack.
c4 in the Maroczy Bind against the Sicilian is a good move.
So you need to understand what the goals of the openings are and what kind of middlegame they get you to.
My friend and I both have different styles of play. He likes to advance his knights so that they're in front of the c and f pawns. I prefer to advance the c and f pawns first and then bring the knights out behind them. This I think gives me a certain advantage in that, for example with the king side, e4 and g4 are defended twice by both the pawn and the knight. In the opening, I think that pushing the pawns first doesn't lose enough tempo to warrant not pushing them - of course it depends on the opening and sometimes I have to adjust my play to take the opponents move into account if there is a good reason not to push them.
Does anyone else have any opinions or statistics that would either enforce or counter this method of play? I particularly like to play this method using the Bird's or Sicilian openings.