It could simply be an evolutionary "discovery", with no particular advantage over our "brain model". Evolution doesn't seek out optima; it simply encourages genetic structures that improve odds of reproductive success.
Or, to put it another way: if corvid genetics happened upon a brain type that promoted their survival, it doesn't matter if it was "better" or "worse" than the path the monkey/hominid brains took. Genetics took the first bus going in that direction.
In terms of why bird brains would be exceptionally efficient for their volume (and I assume by extension, mass), would be that weight is at a premium for them.
Or, to put it another way: if corvid genetics happened upon a brain type that promoted their survival, it doesn't matter if it was "better" or "worse" than the path the monkey/hominid brains took. Genetics took the first bus going in that direction.