Pawn Structure Change in the Pirc - dxe5 or Nxe5? As black I reached this position in a recent game

[White "Somebody"]
[Black "Ian Bush"]
[Result "*"]
[ECO "B07"]
[FEN ""]
[StartPly "23"]

1.e4 d6 2.d4 Nf6 3.Nc3 g6 4.Be3 c6 5.f3 b5 6.a3 Nbd7 7.Bd3 Bb7 8.Nge2 Qc7 
9.Ng3 Bg7 10.Nce2 e5 11.O-O O-O 12.dxe5 dxe5 
    ( 12...Nxe5 )


On running it through the Lichess analysis it reported 12 ... dxe5 as a blunder. This, to say the least, somewhat surprised me, but on sticking it through Stockfish on my own machine the semiconducting monster does indeed markedly prefer Nxe5 - taking with the Knight it puts at ~-0.4 and taking with the pawn +0.25, so over half a pawn swing. I preferred taking with the pawn to avoid having a potential weakness on d6, and also thought his pawn on e4 so well defended that the half open e file was little use to me, so I am struggling to understand why 12 ... Nxe5 is so much better. Can somebody enlighten me? Is it simply to get the white squared bishop for the knight, or is there a deeper strategical meaning? I do understand that taking with the pawn is more unbalancing, and so what I would definitely prefer if needing a win, but I just can't see why it is intrinsically so much better. 

More generally this kind of decision is not uncommon in the Pirc and some related openings, are there any general pointers as to which should be preferred?
It comes down to the VERY poor placement of the white pieces, in particular, that the Bd3 is vulnerable to being trapped by the advancing black queenside pawns. Taking with the knight also allows you to open the center with d5 in some lines (which also will make the Qd1 uncomfortable since it lacks space), taking advantage of your better-placed pieces, and Nxe5 also stops the desirable move c4 by white immediately.

In one of the lines I give below, which sums it up, I wrote: "Black is better developed, and all of his pieces are nicely placed. By comparison, the Bd3 is horrible, the Ng3 is worse, and the Ne2 is no prize horse. The Qc1 is also worse than the Qc7."

 [FEN ""]

 1. e4 d6 2. d4 Nf6 3. Nc3 g6 4. Be3 c6 5. f3 $6 {After this, it is really difficult for white to develop the pieces since the Bf1 does not sit well on d3, and the Ng1 and Bf1 fight for e2.} b5 6. a3 $6 (6. Qd2 Nbd7 7. g4 {Is better, postponing the decision about the Bf1 and Ng1.}) 6... Nbd7 (6... Bg7 {Why not this move that you know you must make? You should make moves that you know you have to make first, since circumstances may change for the others.}) 7. Bd3 Bb7 8. Nge2 Qc7 (8... a6 $1 {Idea c5, and you are already better as the misplaced Bd3 is not well-developed.}) 9. Ng3 $2 {Where is this piece going?} (9. Qd2) 9... Bg7 10. Nce2 e5 11. O-O O-O 12. dxe5 dxe5 $2 (12... Nxe5 $1 {This also stops c4!} 13. Qc1 (13. Qd2 c5 $1 14. c3 (14. Bxb5 a6 15. Ba4 Nc4 16. Qc1 Nxe4 $1 17. Nxe4 Bxb2 18. Qb1 Bxe4 $19) 14... d5 $17) 13... Rfe8 14. Bh6 Bh8 15. Kh1 d5 {Ripping the center open. Black is better developed, and all of his pieces are nicely placed. By comparison, the Bd3 is horrible, the Ng3 is worse, and the Ne2 is no prize horse. The Qc1 is also worse than the Qc7.}) 13. c4 {White is better on the queenside here, and this immediately exposes it to the major pieces of white with either Rc1 soon. White could also try to play against the weakened c5 square with Qe1-f2, and Nc1-b3. That Ng3 still is an ugly piece.} a6 14. Qc2 Rfc8 15. Rfc1 $14