Is there any real difference between avian and reptilian brains, other than relative size, or are the differences a result of scientific bias? For example avian brain anatomy has now its own nomenclature, which is closer to the mammalian, but reptile scientists still use inconsistently avian, mammalian, or amphibian terminology.

You are correct there is a far more detailed description and body of work relating to the avian as compared to reptile nervous system. That presumably largely explains the lack of defined terminology for the latter. The reasons are unclear (at least to me) other than to state the obvious that more scientists appear to be interested in studying birds than reptiles.