Why did black choose 1... Kxg7 instead of 1... Rfe8 in this puzzle? I have a doubt with a puzzle that I solved recently. The proposed solution for that puzzle is as below.

[FEN "r4rk1/pp4np/2n1bppB/qNQ1p3/8/6P1/PP2PPBP/R4RK1 w - - 0 1"]

1.Bxg7 Kxg7 2.Bxc6 bxc6 3.Nd4 Qxc5 4.Nxe6+ Kg8 5.Nxc5


But instead of choosing 1... Kxg7, if black has chosen 1... Rfe8, I think it would have given black a better position as below.

[FEN "r4rk1/pp4np/2n1bppB/qNQ1p3/8/6P1/PP2PPBP/R4RK1 w - - 0 1"]

1.Bxg7 Rfe8 2.Bxc6 bxc6 3.Nd4 Qxc5 4.Nxe6 Rxe6


In a comment below the puzzle, someone has mentioned that if black doesn't take the bishop, it loses a minor piece. What is that referring to? Is there any specific reason for black not choosing 1... Rfe8?
I've done this puzzle today too! It's Chess.com's puzzle of the day =)

I have analysed it with Houdini 3 Pro. Here is what it says after 1.Bxg7 :


1...Kxg7 : +5.07
1...Rf7 : +5.43
1...Rfe8 : +5.52


After 1... Rfe8 your move 2. Bxc6?? is a blunder and lose a lot of White's advantage (White is still probably winning but not by much). Houdini evaluates it as only +1.96

The killer move is 2. b4!! which Houdini evaluates as +5.52

It will continue: 2... Nxb4 3. Bxf6 Rac8 4. Qxe5 Bc4 5. Be7

(It's pretty much forced, all other Black replies are much weaker. 3... a6 is answered by 4. Qc7 ; while 2... Qd8 is answered by 3. Rfd1)

Then here are three lines:


5... Bf7 6. Bxb4 Qxb4 7. Rab1 Qxb1 8. Qxe8+ Rxe8 9. Rxb1 Rxe2 
5... Qd8 6. Bxd8 Rxe5 7. Nd6 Rxd8 8. Nxc4
Rxe2
5... Qxb5 6. Qxb5 Bxb5 7. Bxb4 Bxe2


According to the omniscient Houdini the move 1...Rfe8 is technically slightly inferior to 1... Kxg7. But I think you are right: if it was a practical game, Black should play 1... Rfe8 because it gives White a harder time at finding the correct optimal continuation.

Trading Queens with 1... Kxg7 simplifies the position and makes it very easy to win for White. But after 1... Rfe8 the position is still complex and White may make a mistake. I believe Black's best hope is to play 5... Bf7 6. Bxb4 Qxb4 7. Rab1 Qd2?! which keeps the Queens on the board.