I also play the Classical and to me Bb5(+) is THE Anti-Sicilian. It seems that on most levels the "hybrid" line 2...Nc6 3.Bb5 d6 and 2...Nc6 3.Bb5 e6 give Black the most winning chances statistically. So naturally I have chosen the 2...Nc6 move order in order to have both potentially available (I play the Sicilian for winning chances, after all!).

3...d6 gives White a choice of sharp lines that require some memorization from Black (i.e. 4.Bxc6 bxc6 5.0-0 e5 6.c3 f5!? and 4.0-0 Bd7 5.c3 Nf6 6.Re1 a6 7.Bxc6?! Bxc6 8.d4), and the positional main lines with Ba4 or Bf1, where Black scores OK but to me the White position often feels easier to play; he just puts his pieces where he wants them and finally pushes d3-d4. I play 3...d6 now, but wins in tournament games are few and far between.

3...e6 is played by such enterprising GMs as Shirov, Carlsen, Shabalov, Krasenkow etc, but I've long enjoyed White's position after 4.Bxc6 bxc6 5.d3, and I struggle to convince myself to take Black there. Probably I will switch to this eventually.

If all else fails, there is always the ultimate bust to 3.Bb5: Learn a 2...e6-compatible Sicilian! 

In fact 2...Nc6 also can lead to the Dragon and Scheveningen: 5...d6 6.Be2/6.g3 g6/e6.

The only difference in playing ... d6 or ... Nc6 is the Bb5 variation,
I play the classical sicilian too, I play ... d6 first (as recommended), but I think after Bb5+ the game gets quite dull,
unlike in the Nc6 Bb5 variation.
I think if black aims for the win he should play Nc6 first,
shouldn't he?

When playing the Sicilian I aim for the classical variation and I have a move order question.  Is it preferable to play 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 Nc6 or 1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 d6?  What are the advantages/disadvantages? Does one move order avoid more "anti-sicilians" than the other?

Thanks