Do you have an older edition of Vukovic, or the newer one edited by Nunn? The original became infamous for the number of errors with the introduction of the computer analysis age. And Nunn corrected most of them. It's possible some went through, however. Could just be one of them.
Question about "The Art of Attack in Chess"

Not sure whether it's "winning" exactly...but White certainly has a considerable advantage there (I definitely wouldn't want to be Black).
OK, can I ask why?

Do you have an older edition of Vukovic, or the newer one edited by Nunn? The original became infamous for the number of errors with the introduction of the computer analysis age. And Nunn corrected most of them. It's possible some went through, however. Could just be one of them.
Newer one. He didn't mention it.

OK, thanks. I was aware they were better but I thought it would only usually be very slightly.
Can one of you also explain to me exactly what is inherently better about the 2 minor pieces?
Cheers.

Um... Uhhhh.... Errrr... I hate to say this but if my engine analysis is correct it contradicts received wisdom here. (And FWIW... My instincts were totally in-line with what all the humans here have been saying: "two minors better than a rook, rather distinctly" -- I turned on the engine with the idea that I would show how when it's GM vs. GM the two minors make mincemeat of a lone rook...but, here...
It doesn't work out that way... the engine draws. Surprised... I plugged the OPs position in and looked at the evals for the analysis given by Vukovic/Emms (first checking with my own copy of Vukovic that the OP had transcribed the moves correctly... he has.) ...So, this Emms' fixed version? Jeez... Vukovic/Emms gives 3.Qe2! (exclam?... actually it deserves a ?! at best) it's only an exclam because the response 3...Re8? is a game losing blunder as demonstrated by the remainder of Vukovic's analysis.
According to Stockfish, the OPs idea 3...Qd7 is correct, with equality (for those with engine-level technique, anyway) in a R+p v two minors imbalance.
HOWEVER... 3.Qe2?! is wrong in the first place... 3.Qd2! is winning and is a correct refutation of 1...0-0 (in a line that finesses its way into looking a whole lot like that Re8 line.)
Freaking computers.

lol, I was wondering why not Qd2 immediately, and thought if Qe2 was so good, there was something subtle, and I didn't want to burn my brain trying to figure it out.
That said, I don't think the line given with the two minors vs the rook is best play perhaps... especially going in for trading off a pair of rooks seemed wrong to me. Running it though Rybka3, white keeps an edge (+/=) by playing 7.d5 instead of the 7.c3 move. (and also will not trade rooks heh).

lol, I was wondering why not Qd2 immediately, and thought if Qe2 was so good, there was something subtle, and I didn't want to burn my brain trying to figure it out.
That said, I don't think the line given with the two minors vs the rook is best play perhaps... especially going in for trading off a pair of rooks seemed wrong to me. Running it though Rybka3, white keeps an edge (+/=) by playing 7.d5 instead of the 7.c3 move. (and also will not trade rooks heh).
I should have mentioned that it's NOT best play for Stockfish. It's what I played trying to arrive at a simplified position to highlight the R vs two minors... when I checked it with the engine I was pleasantly surprised to discover that although it wasn't first choice best all the way, I hadn't done so bad at all, so I left it.
Vukovic's recommended move here is 1.Bf6 (other tries like Qe2 don't work due to Kf8). He says it stops Black from 1...0-0 due to 2.Rxe7 Nxe7 3.Qe2 which is supposed to cleverly lure the Rook away from f8 (3...Re8 4.Qd2 Kh7 5.Ng5+ Kg8 6.Ne6 fxe6 7.Qh6 etc.).
But my question here is that is the threat of winning the Knight on e7 really a decisive one? For instance 3...Qd7 4.Qxe7 Qxe7 5.Bxe7 Re8, is that winning for White? I can't see that it is.