As others have pointed out, having your center pawns side-by-side is almost always the best configuration. Pushing one of them will often result in weak squares / holes, and may also lose time if they just end up getting traded.
When being on the same rank, they harmonize better at controlling squares in your opponent's camp, and they allow you to always threaten (!) to push one of them. However, these "threats" are usually much more important than their execution.
That is because by having a pawn center, you are basically "threatening" 3 things at once: Pushing the left one, pushing the right one - or leaving them as they are. As soon as you actually do push one of the pawns, this flexibility is gone; your opponent will from now on know what the structure is gonna look like, and not have to be prepared for 3 different kinds of structures all the time.
Because of this, you should only push one of them, if you gain something very concrete (or if your opponent managed to force you to do so.)
In the example you gave, leaving the pawns as they are (or maybe even creating a pawn trio with 12...c5) is therefore a good idea.
However, pushing the e pawn is also very good: After 12...e4 13. Ne2 for example (trying to "exploit" the weaknesses created by your pawn push), 13...Ng4 followed by Bd6 (threatening Q(x)h4), will force white to play g3, after which you will have Ne5 followed by Nf3+ with a strong k-side attack. Also note that you're locking out white's bishop with 12...e4, making it more difficult for him to coordinate his minor pieces for an effective defense.
When being on the same rank, they harmonize better at controlling squares in your opponent's camp, and they allow you to always threaten (!) to push one of them. However, these "threats" are usually much more important than their execution.
That is because by having a pawn center, you are basically "threatening" 3 things at once: Pushing the left one, pushing the right one - or leaving them as they are. As soon as you actually do push one of the pawns, this flexibility is gone; your opponent will from now on know what the structure is gonna look like, and not have to be prepared for 3 different kinds of structures all the time.
Because of this, you should only push one of them, if you gain something very concrete (or if your opponent managed to force you to do so.)
In the example you gave, leaving the pawns as they are (or maybe even creating a pawn trio with 12...c5) is therefore a good idea.
However, pushing the e pawn is also very good: After 12...e4 13. Ne2 for example (trying to "exploit" the weaknesses created by your pawn push), 13...Ng4 followed by Bd6 (threatening Q(x)h4), will force white to play g3, after which you will have Ne5 followed by Nf3+ with a strong k-side attack. Also note that you're locking out white's bishop with 12...e4, making it more difficult for him to coordinate his minor pieces for an effective defense.