Human brains might not be all that efficient; for example, if the competitive edge for primate brains is distinct enough, they'll get big before they get efficient. And humans are a pretty 'young' species. (Look at how machine learning models are built for comparison... you have absolute monsters which become significantly more efficient as they are actually adopted.)
By contrast, birds are under extreme size constraints, and have had millions of years to specialize (ie, speciate) and refine their architectures accordingly. So they may be exceedingly efficient, but have no way to scale up due to the 'need to fly' constraint.
By and large It’s not direct competition but we are stamping our species at an alarming rate and birds are taking a hammering.
There's too many confounding factors to say that the human brain architecture is actually 'better' based on the outcomes of natural selection. And if we kill all the birds, we will lose the chance to find out as we develop techniques to better compare the trade-offs of the different architectures.