According to the Game Database of ChessTempo, the mainlines of 6...Bb4 and 6....Be7 are quite similar:
- 6....Be7 7.cxd5 Nxd5 8.Bd3 Nc6 9.0-0
- 6....Bb4 7.cxd5 Nxd5 8.Bd2 Nc6 9.Bd3 0-0 10.0-0
Remarkably, the main move for the second line is 10....Be7, which transposes to the first line, but with an extra Bd2 for white. For instance, Nakamura-Wojtaszek and Motylev-Jakovenko.
Instead of 7.cxd5, white can also play 7.Bd3. In this case it is difficult to tell whether the bishop is better placed on b4 (to have the possibility to take on c3) or on e7 (to protect against the pin after Bg5).
Edit by Evargalo: The logic behind Black wanting the White bishop on d2 and not c1 is a bit complicated: In the variations with the bishop on c1, the main line (after 9.0-0 Nc6) is the logical 10.Re1, where there is a lot of theory and Black has to work hard to equalize. With the bishop on d2, however, 11.Re1?! is a dubious pawn sacrifice after 11...Ndb4! 12. Bb1 (or Be4, or Bf1, or Bc4) Nxd4, because the Bd2 interferes in the Qd1-Pd4 connection. Thus the main lines are 11.Qe2 or 11.a3, which are less direct although the opening debate remains open to this day.
Objectively speaking, the values of 6....Bb4 and 6....Be7 are probably similar. Therefore, choosing between both moves is more a matter of taste.
Note that the position after 6....Bb4 can also arise after a transposition from the Nimzo-Indian, which is the subject of another Stack Exchange question.
1.e4 c6 2.d4 d5 3.exd5 cxd5 4.c4 Nf6 5.Nc3 e6 6.Nf3 Bb4 (6...Be7 7.cxd5 (7.Bd3) Nxd5 8.Bd3 O-O 9.O-O Nc6 10.Re1) 7.cxd5 (7.Bd3) Nxd5 8.Bd2 Nc6 9.Bd3 O-O 10.O-O Be7 11.Re1?! (11.Qe2) (11.a3) Ndb4 12.Be4 Nxd4