It depends on the mythical species, but there is variation.
In the world of Mino Hotel, for example, there are different lineages of gryphons, just like humans have race and ethnicity. Despite Luke's alleged Greek heritage, genetically he's overwhelmingly native American in origin (from his mother's side) and mixed (from his father's side). But he does descend, distantly, from the Nemean Lion.
Grootslangs, on the other hand, have less variety because they were almost exterminated by the gods long ago. They try to keep themselves close-knit and discreet, so there aren't enough of them for their community to grow genetically vibrant.
Anyway, even then some traits may skip a few generations instead of disappearing. It's safe to say that, yes, some will be more animal-like or more human-like than others. Oscar and Asterion are a good example of that, as they are different anatomically in a very specific way. And some will have more magical properties too! Luke had more magic juice than his brothers, and Khenbish too.