I have played both systems and the following is based on my own experience and not from a publication.
There is subtle fact about central pawn pushes. Let me illustrate this with an example. Let us say we want to control the dark squares in the center. Imagine the two cases:
With central pawn push. With d4 push your Queen has influence on d4 square. (Similarly, if you have a pawn on e4 and a rook on e1, then that rook's influence reaches e4.) Now, if the N appears on its natural square on f3, then you have two hits at the e5 square and two on the d4 square: Q + N (but not the pawn which does not protect itself!)
Without central pawn push. Suppose we want to obtain the same control on d4 and e5 with non-central pawn pushes and pieces only. I tried the following set-up for the fun of it in my Blitz games (with good result in fact!): 1.f4, followed by Nf3. This achieves the two hits on the e5 square but the d4 square is hit only once, by the N. To add more without a central push, one fianchetos the Bishop. But this takes two more moves: b3 and Bb2. This gives two hits on d4 and three (B, N and pawn on f4) on e5.
So, central pawn advances bring FASTER control to the central squares from the pieces (two moves versus 4 moves in the examples).
I have decided for myself that pushing pawns to the center when allowed with either color is often easier to play.* Other than the reasoning above here are some more advantages that I can think of for pushing pawns in the center as early as possible:
- Faster development: Bishops open up immediately,
- Restricting opponent options, (In the above example of 1.f4 Black even has the sacrifice 1.e5 which is very good for them.)
- Pawn that are in the center themselves control the two squares that they attack,
- Fianchetoing bishops weaken the pawn structure on the flanks, specially on the side where you will castle.
- Sicilian is an exception to me, although there again I have recently opted to play the Sveshnikov (this e5 push) which despite giving the hole on d5 gives me good control in the center and I found easier to play than say the Najdorff.