What would be your move

take the dsquared bishop

WHY

Rf1

No no Rf3

@Mannequin08 , delete your comments please, there's X button

NxBe3 because the problem with Rc1 is that it's being defended by Be3, if you remove the defender, he's forced to take with pawn and you can slide Rc1, pinning the queen

1...Nxe3 2.fxe3 (otherwise lose a queen) Rc1

Idk I understand that the engine prefers Nxe3 and that might be good strategically but to me Nc3 looks much more interesting and straightforward - making a fork, winning a rook

Let's see the starting position. Black is a piece up for a pawn. d5 knight is attacked 2 times. Let's say black doesn't see the tactic but notices that the knight will be lost if something isn't done with it. So, I don't know, something passive like Ne7.

Why am I talking about this pretty sub par move? Because with that move black is still winning.
So any move that wins further material is winning more easily. But any further gain of material is diminished.

With Nc3, you win an exchange. Queen doesn't have to go to b1 to defend the rook. Nc3, then Qb3, Nxb5, Qxb5 is an exchange. In the end position you are a rook up for a pawn. That is 4 points of material more.

Nxe3 is a check and it attacks a queen, so white has to take. This is a relatively simple removing of the defender tactic. Now Rc1 wins the queen for the rook. In the end position you have a queen and the knight for a rook and the pawn. That is 6 points of material more. Plus it leaves less material on the board for white and gives him less chances. On the other hand, it kind of disbalances position which is better if you are trying to get back from a lost position.

Still less material on the board means more simplicity in most cases, so with more material gain along with it, Nxe3 is better. But as I've said, both are very good.

Now one more thing. If the position at the start was equal, Nxe3 would be much better than Nc3, because queen for the rook is much easier to win than simply with an exchange up.

It's not a bad move by any means but you win less material that way.

Nc3, forking the Queen and Rook. The only square the Queen can go to in order to protect the Rook is b3 (the Knight covers b1), and NxR QxN puts them down the exchange (as QxQ leads to NxQ, and Black is up a full rook). Black can then capture the a pawn with their Queen, giving them the only Queenside pawn, and good open files on that side for their rooks to infiltrate on and/or give aid to the Black a pawn to start creating a worry for white.

Is this some Kramnik style research to see if the engine move is obvious for a human? It is obvious here, nxe3 wins the most material following up with pinning the queen. The other option nc3 is met with qb3 losing only the exchange for white.

Oops, yes, Nxe3, I missed that the rook is now free to go to c1.

Yeah, you can even win that pawn after Nc3. So it is only one point of material difference. 
But as I've said, the problem of the position is that everything is winning. Even with a sub par move like Ne7, it is winning because of the starting material advantage and the weakness of the white king.

So the starting advantage is even more pronounced than a piece for a pawn (which in itself is winning).