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<20... Nd7??> was a blunder but white missed to play the better <21.Qh4 >

I don't know how extensive the line with 9...gxf5 10.gxf6 has been analyzed. Opening Explorer has 72 games with 9...gxf5 10.exf5 and only one, Ljubojevic vs Polugaevsky, 1992 (a draw) with 9...gxf5 10.gxf6. The more comprehensive 365Chess.com big opening database has 141 games with 9...gxf5 10.exf5 (White wins 50.4% of the games, Black wins 28.4% of the games, and 21.3% of the games are drawn), and 8 games with 9...gxf5 10.gxf6 (White wins 37.5% of the games, Black wins 50.0% of the games, and 12.5% of the games are drawn). So it seems that Black does better in the 9...gxf5 10.gxf6 line, even thought the small number of games makes it difficult to reach a definitive conclusion, and you also need to take the players relative ratings into account.

The more exclusive 365Chess masters opening database has 74 games with 9...gxf5 10.exf5 (White wins 43.2% of the games, Black wins 27.1% of the games, and 29.7% of the games are drawn). And the only game with 9...gxf5 10.gxf6 is the same Ljubojevic vs Polugaevsky, 1992 game.

The ChessTempo masters opening database has 129 games with 9...gxf5 10.exf5 with similar statistics (White wins 46.5% of the games, Black wins 25.6% of the games, and 227% of the games are drawn). And it has 3 games with 9...gxf5 10.gxf6, the Ljubojevic vs Polugaevsky, 1992 game, plus Bulanov vs. Omariev, 2010 (0-1) and E.Dominguez vs. C.Barrero Garcia, 2005 (1-0). Bulanov (2379) had a 68-point rating advantage over Omariev (2311) and Dominguez (2351) and Barrero (2337) were fairly evenly matched, ratings-wise.

So it looks like 9...gxf5 10.exf5 gives White more practical chances than 9...gxf5 10.gxf6, even at the master level. Here is a game collection, Game Collection: Show in the Opening: Perenyi Attack, consisting of 9 GM-level games, with a White winning % of 90%!

But the most recent game from that collection was played in 2006. What do the computers now say about the two main alternatives after 9...gxf5, 10.gxf6 and 10.exf5?

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Well, here is some analysis from two top engines:

Komodo 8, d=29:

1. [-0.89] 10.gxf6 f4 11.Bd2 Nd7 12.Rg1 Nxf6 13.Qf3 h5 14.h3 Qb6 15.Rb1 Be6 16.Bd3 Qd4 17.Kd1 Rc8 18.Kc1 b5 19.a3 Rh6 20.Rd1 Qc5 21.b4 Qd4 22.Ne2 Qa7 23.Nc3 Be7 24.a4 Qd4 25.axb5

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White allowing the weakening of his q-side around his king y 19.a3, 21.b4, and 24.a4 looks unwise, and Black has seemingly sacrificed a pawn to further open lines on the q-side. But Black's Rh6 is out of play and it will take some doing for it to get to the q-side to participate in any q-side action. And after 25...axb4 26.Bxb5+ Kf8, Black's king seems relatively safe and Black is ready for ...d5, opening up additional lines (and possibly allowing the Rh6 to get to the q-side).

2. [-1.41]: 10.exf5 d5 11.gxf6 d4 12.Bc4 Qc7 13.Qd3 dxc3 (here Komodo deviates from Polgar) 14.bxc3 Bxf5 15.Qxf5 Qxc4 16.Qxe5+ Qe6 17.Qxe6+ fxe6 18.Rb1 b5 19.a4 Nd7 20.axb5 axb5 21.Ke2 Rb8 22.Rb2 Nxf6 23.Rhb1 Bd6 24.Rxb5 Rxb5 25.Rxb5 Bxh2 26.Rb7 h5 27.c4 Rh7 28.Rb6 Kf7 29.f4 Rh8 30.Rb7+ Kg6 31.Rb6 Re8 32.Kf3 h4 33.Bf2 Kh5

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Komodo deviates from Polgar with 13...dxc3 instead of 13...dxe3 and I think that's a better approach. White's Nc3 has a better potential on d5 than White's Be3, and have you ever seen a worse pawn structure than White's after 14.bxc3? After the queen exchange White's attack is probably over and Black has a knight for 2 (miserable) pawns and better chances in the endgame.

Stockfish 6, d=37:

1. [-1.09]: 10.gxf6 f4 11.Bd2 Nd7 12.Nd5 Rg8 13.Bc4 Nxf6 14.Qf3 Be7 15.Nxf6+ Bxf6 16.Qb3 Qc7 17.Ke2 b5 18.Bd5 Bb7 19.Rhg1 Bxd5 20.Qxd5 Ke7 21.Rac1 Rxg1 22.Rxg1 Rc8 23.b3 Qb6 24.c3 Qc7 25.Rg2 Rb8 26.Rg1 Qc8 27.Qd3 Qc5 28.Qd5 Qxd5 29.exd5 Rc8 30.Kd3 Bh4

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Stockfish hurries to occupy the critical d5 square but I wonder about its choice to forego 0-0-0 which would have better defended the q-side pawns and allowed more pressure against d5. In the final position Black is a pawn up and has the more active pieces, and after ...f5 his central pawn mass will be ready to advance.

2. [-1.60]: 10.exf5 d5 11.gxf6 d4 12.Bc4 Qc7 13.Qd3 dxc3 14.bxc3 Bxf5 15.Qxf5 Qxc4 16.Qxe5+ Qe6 17.Qxe6+ fxe6 18.Rb1 b5 19.a4 Nd7 20.axb5 axb5 21.Ke2 Nxf6 (here Stockfish deviates from Komodo) 22.Rxb5 Rg8 23.Rb6 Kf7 24.Rb7+ Be7 25.Bc5 Nd5 26.c4 Rgb8 27.Rxb8 Rxb8 28.Bxe7 Nxe7 29.Ra1 Kf6 30.Kd3 Rd8+ 31.Kc3 Rc8 32.Ra6 Nf5 33.Kd3 h5 34.Rb6

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Stockfish, like Komodo, also captures 13...dxc3 to eliminate White's potentially powerful knight and weaken White's hold on d5. In the final position White has 2 passed but isolated pawns for his knight, and it will be hard for White to defend his k-side pawns from Black's rook after 34...Rg8. Restarting the analysis from this position Stockfish evaluates the resulting position at [-3.11], d=37 after 34...Rd8+ 35.Kc3 Rd4 36.c5 Ke5 37.Rb8 Kd5 38.Re8 Rh4 39.c6 Nd6 40.Re7 Nb5+ 41.Kd3 Rh3+ 42.Kd2 Kd6 43.Re8 Nc7 44.Rf8 Kxc6 45.c4 Kd6 46.f3 Rxh2+ 47.Ke3 Na6 48.Rd8+ Ke7 49.Rh8 Nc5 50.f4 Rh4 51.Kf3 Nd3 52.Kg3 Rxf4 53.Rxh5 Rxc4 54.Ra5 Kd6 55.Kf3 Ne5+ 56.Ke3