I played the Bd7 line in a few games with white and black. With white I had an easier game in the maroczy positions with a black bishop on g7. With a bishop on e7 blacks position is really stable here, I dont think white has besser chances in this case (e.g. in the line you suggested). So with black I generally prefer e6 systems in the Bb5,Bd7 lines.

I won't claim an advantage for White - that would mean that 3.Bb5+ is better than 3.d4, a point of view I would not like to defend. But I have played this type of position (after 10.c4) a few times and found it rather easy to play. His plan is quite simple: prevent ...d5, finish development (the bishop goes to b2) and gradually prepare an attack.

Of course Black in the Open Sicilian can avoid the Maroczy Bind so this is one plus of 3.Bb5+. Moreover White has still the option of going for the big centre with c3/d4. And White still has a smooth development.
When I used to play the Bb5 systems my thumb rule was to play the Maroczy Bind if Black choose a Scheveningen setup (e6, Be7) and c3/d4 after a King's Fianchetto. This is a choice White definitely does not have in the Open Sicilian.
Eg 1.e4 c5 2.Nf3 d6 3.Bb5+ Bd7 4.Bxd7+ Qxd7 5.0-0 Nc6 6.Qe2 Nf6 7.Rd1 g6 8.c3 Bg7 8.d4 or 7...e6 8.d4 cxd4 9.Nxd4 Be7 10.c4.

I always thought that Bb5+ was designed so to allow for a Maroczy Bind (c4) without the Bishop caged in. In my opinion this Bishop is useful for the Bind even when it is caged in, as it helps against Black's pawn breaks (e.g. directly vs. b5 or indirectly vs. f5, since when the position opens up this piece will show its powers).

On the other hand when I face Bb5+ as Black, I find it difficult to create winning chances as 3. ... Bd7 is too symmetrical, while 3. ... Nbd7 is a bit risky.

So, maybe White is using this variation as a suggestion for a rsik-free, rather drawish game.

I don't understand the move Bb5+ after 1. e4 c5. 2. Nf3 d6. There won't be any doubled pawns or other serious concession and it actually looks like White loses a tempo while trading off a piece that could have been key to his initiative (doesn't trading pieces lessen his development advantage?) or maintenance of a space advantage. The position after 3. Bb5+ Bd7 4. Bxd7 Nxd7 is exactly as if we looked at the position after 2. ...d6, removed the light squared bishops from the board and gave Black the move Nbd7. The problem is that after 2. ...d6, it was White's move! It's true the knight is not as well placed on d7 as c6, but is it really better on b8? Similarly, Black can play Qxd7. Perhaps it's not the optimal square but the knight can develop to c6 and the rooks are connected upon castling. Again, is it really better on d8? The first time I saw Bb5+, I thought it was just stupid and silly with little point except to avoid theory.   

After looking at it more, I see some plusses for White:

1. Black doesn't gain a full tempo since the recaptures are slightly suboptimal.
2. Early development of the light squared  bishop is often a problem for White in the Sicilian. It's a bit passive on e2, can be kicked around and blunted on c4 etc. Any early development of the light squared bishop will offer Black a flexible way to deal with it adequately. Moreover, if White tries to just squeeze black in a bind with c4, b3, f3 etc., it might not help him to have the bishop stuck behind the pawn chain even considering that exchanges lessen the cramp on Black. If one does not go for the Open Sicilian, there aren't many ways to flexibly delay development of this bishop. For example, g3 reveals the plan early, Nc3 blocks a possibly useful central pawn in a position where f4 can't be played and the Open is not the plan etc. As such, White can trade it off and gets castles as a waiting move and forces Black to show his cards a bit with his recapture.
3.  Patzer see check, patzer play check! I'm out of ideas.

Of course, I only covered Bd7 and I'm still lost. Please help me better understand this move! What are its objective merits - pros, cons etc.?  How would it compare to Bb5 after Nc6?

Thanks in advance!