Here are presented fundamental differences between the DDG and the BDG, in hope that BDGers would find new viewpoints, and maybe even try the DDG. Many BDGers play the Alapin French 1.d4 d5 2.e4 e6 3.Be3, so an easy way to try the DDG is to play 3.c4 every now and then.
At first, the BDG Euwe Defence looks the most similar to the DDG: Black plays like in the French Defence, that is, e6 before freeing the Queen's bishop. The only difference is that White plays c4 before Nc3 in the DDG.
White can play Bc2. When c2 is no longer occupied, White can play the queen to it, or the bishop via d3. The ultimate threat is naturally h7 if Black castles kingside. The same effect is achieved in the BDG by playing the bishop to d3 and manoeuvreing the queen to h4 via e1, or sometimes to h3 via f3.
White can play d5 freely. Black usually does well in trying to break the center, with timely c5 or e5. White can then, however, rather safely play d5 which is supported by the c4-pawn. Note that d5 is more dubious in the BDG. For example, after 1.d4 d5 2.e4 dxe4 3.Nc3 c5 4.d5, White can attack d5 which is difficult to defend.
Black cannot play Nd5. The c4 move simply strengthens the center. Black may not play Nd5 often in the BDG, but it would especially annoying if White's bishop is on e3. The grand Diemer once played c4 in the Alapin French: 1.e4 e6 2.d4 d5 3.Be3 dxe4 4.Nd2 Nf6 5.c4, 1-0 in 38, Diemer - Johansson, 1958.
White cannot play the bishop to c4 or b5. This may be the main reason why BDGers consider the DDG odd. From an attacking point of view, the f7 square is hardly ever an issue in the DDG because the bishop cannot easily threaten it.
White can seldom castle on queenside safely. White's queenside is ragged when c2 is not occupied. If Black manages to play e5 and Bf5, White's king on c1 is in a real danger.
Black can play Bb4 freely. Now that White can no longer play c3, Black's bishop can come to b4 without fear.