I was going to say the same as paul.
As an extra point, we can't give you a general rule for all points in the game because it will always depend on the position of the board
Do you defend a pawn with a knight or a pawn
Sort:
In general, you want to tie down a piece of lesser value to defense. It's worth pointing out though that in your diagram neither move will tie down a defender, because as the game goes on it's likely other pieces will defend e5 / e5 will be traded off.
But also in general, good moves do more than 1 thing for your position. Nc6 develops a piece and defends the pawn. The other positives are noted by paul e.g. doesn't block the bishop.
In your diagram, both are known opening moves. d6 is considered solid but passive while Nc6 can lead to many different and complex types of positions. For that reason you'll almost always see Nc6 from very strong players.
Given the following two data points:
- After 1.e4 e5 2.Nf3, black's best [move which defends e5] is 2...Nc6
- After 1.d4 d5 2.c4, black's best choices are 2...e6 and 2...c6
One rule could be when a pawn is attacked with a pawn, defend with a pawn. When a pawn is attacked with a piece, defend with a piece.
Too simplistic, I know. In the middlegame, tactics will dictate which is best. In the opening, really you should just know. If you don't, try one and then the other, see which one works better for you.
why should i defend my e5-pawn?
no defence...offence!
2...f5 or 2...d5!
In those two cases, I think it's better to attack the e4 pawn with a piece, not with a pawn.
Ah, quite so. When your pawn is attacked by pieces, counter attack with pieces. When a pawn is attacked by a pawn... oh never mind this is just silly 
For example, in this common situation:
Does black play d6 or Nc6. If you can, try to give guidelines for when to defend with a knight and when to defend with a pawn.