During a recent game, I was faced with this option.  I decided not to try it, but I wonder how it would have turned out.  At this point, the game is fairly even.  I normally don't play that aggressively, but I did think long and hard about trading my knight for 3 pawns.  What would you have done?

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Depending on the position and keeping all other things constant, I wud say that more the open the game is (unlocked pawns) and more the game is inching towards the endgame, pawns increase in strength. So i might go for the trade of a knight for 3 pawns.

In openings, 1 Knight ~ 3 pawns, 1 Bishop ~ 2.5 pawns

In advanced middle game and endgames, 1 Knight ~ 2 pawns, 1Bishop ~ 3 pawns

These are just my opinions though.

I would trade the knight for three pawns for positional advantage and the black king is still in check.I feel it is a pretty good trade for a position that favours white

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Wouldnt you lose the rook with Bxg8. The bishop on c4 I mean.

I am talking about the white bishop on c4 which will take the black rook on g8 in your line. 4 Bxg8

1 Nxe5 de 2 Bxe5 Be6 3 Bxg7 Rg8

It sounds like a cool thing to do but just like any other exchange, there's a time and a place.

I can't remember the last time I got to pull a Rxf3.

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I am talking about the white bishop on c4 which will take the black rook on g8 in your line. 4 Bxg8

1 Nxe5 de 2 Bxe5 Be6 3 Bxg7 Rg8

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My bad, Apologies.

I feel like

1.Rde1 0-0-0
2.Nxe4 dxe4
3.Rxe4

would be an interesting direction