We know, for a fact, that biological brains work. Not only do they work, they work enormously well learning and adapting based on dramatically less available data, utilizing vastly less resources than anything we've conceived of in artificial computing.
Biological architectures may not be the best possible, but empirical evidence demonstrates that they can result in intelligences ranging all the way up to sentience.
The question is if its appropriate to compare logical machines, which are built on things secondary, a-posteriori to the primary aspects of human cognition--that is to say logic--with the primary, biological, a-priori aspects of cognition which are in some sense inscrutable. I myself do not believe that we will never be able to comprehensively understand the way in which our minds work, only religion leaves mysteries up to God. But I think that using scientific empirical logic to understand how we are able to perform judgements such as those made with scientific empirical logic will never yield the proper result; judgement itself must be investigated. Something I don't think many researchers in the field of neural-networks are capable of doing.
> Is there any reason to believe that biologically inspired architectures should yield better performance ?
At the very least, they could yield far better efficiency. A 12W brain can achieve more an entire data center of GPUs, depending on what you are trying to achieve. Whether that would make something actually demonstrate sentience level performance is another question.
One might argue that CNN are biologically inspired, but it's more likely that the reason they work is because they respects input symmetries