Comparing 6.Bb3 and 6.Bc4, the drawbacks of the latter are obvious since the bishop is not protected and can become a target to attacks:
either by a black piece: Ne5, Na5, Qc5, Qd4...
or, more probably, by the d-pawn: the typical ...d5 will gain a tempo for development
On the other hand, I can see no advantage of having the bishop on c4 rather than b3. You will hardly ever want to retreat to e2, nor to play a queenside fianchetto.
Given how important each tempo can be in such an complicated line, it is understandable than no strong player has ever ventured 6.Bc4. Probably there isn't a direct refutation, but you might regret having your bishop exposed later on.