Centre pawn vs. side pawn? Chess theory suggests that pawns whose file is nearer to the central files are more powerful. This is somewhat obvious for the rook's pawn, which can attack only one square as opposed to the other pawns, which can each attack two squares. However, in practice, even the rook's pawn turns out to be somewhat useful as a pawn at a3 or h3 can deter the opponent bishop coming to b4 or g4. 
In practice, are the pawns on central files really more powerful than the pawns on the side files? What is the reason? Does the situation change during the end game as opposed to the openings?
The more pieces on the board,  the more powerful the center pawns. This is typical for most opening and middlegame positions. The most convenient place for pieces to travel is usually through the center of the board, and the center pawns help to control that area.

The less pieces on the board, the more powerful the wing pawns. Less pieces on the board means less need to control pieces travelling through the center. A passed wing pawn is harder to stop than a passed center pawn. Your opponent needs to go further to the edge to defend against it. This can really stretch out and discoordinate his pieces if he has to defend against another weakness on the other side of the board. The outside passed pawn is like a decoy.

Generally speaking, you can think of Center pawns becoming weaker and weaker as pieces are exchanged, and wing pawns stronger the closer you reach an endgame.