Put it this way...
The Evans Gambit:
The Evans gambit isn't equal, it's imbalanced.
The Evans gambit is a pawn down compared to the other line, although the Evans gambit has a space advantage.
My point is that in the line you've offered, White gets ALL the advantages that the Evans Gambit offers WITHOUT sacrificing a Pawn. In effect, he's playing an Evans Gambit, a Pawn up.
In the Big Database (with players of all strengths included), the Evans scores 47.3% White wins, 18.9% draws, and 33.8% Black wins. Total: 56.75% for White.
In the Small Database (Master games only), Black does better (30/38/32, total 52% for Black) but those numbers are still well inside the "Equal" range.
The line you suggest (1. e4 e5 2. Nf3 Nc6 3. Bc4 Bb4) scores 74.6% White wins, 10% draws and only 16.6% Black wins. Total: 79.4% for White. It isn't in the Masters database at all, since it's so obviously a bad move.
The missing pawn in the Evans gambit is also it's greatest strength, the line I have shown with the pawn still being there as opposed to its absence plays differently to the Evans gambit.
The fact that the Evans gambit is missing a pawn gives it a space advantage as well as an activity advantage that 1.e4 e5 2.nf3 nc6 3.bc4 bb4 4.c3 doesn't have, therefore it isn't necessarily superior to the Evans gambit for white.
And how does your theory address the FACT that White gets 56% results in the Evans but over 79% results in the line you've offered?
Statistics don't measure an openings strength.
Is 1.e4 e5 2.nc3 nf6 3.bc4 bb4 4.c3 a very poor defense for black, in other words black is left with a very poor defense?
Yes.
You still haven't told us what you hope to accomplish with 3. ... Bb4.
What do you hope to achieve with the move?