There is often a debate on which one of the senior students of Chojun Miyagi Sensei is the most authentic, who has the correct kata?
I go into this question quite a bit in one of my books but have been pondering it more lately.
I think the question of who has the correct version of Gojuryu could be a complicated one. You have the seniors that trained with Miyagi at different times in his development, then you have the years of their own training and discovery after Miyagi passed way to consider. There are a multitude of factors that one could consider in trying to form a hypothesis or prove a theory .
I think that Miyagi Sensei was probably in a constant state of discovery, his karate was ever changing, as his understanding and knowledge advanced, so too did his karate. The seniors all trained with him, at different times in his life, at different times of his understanding.
I am in my 41st year of training in Gojuryu. I can say this if you took all my black belts and put them together and asked them to show you their karate, it would be different.
My karate is no where near the same as it was when I started, it has evolved as I have learned and trained. My teaching methods have changed over the years, as my understanding has changed.
Therefore I think that the answer is this, they are all doing a version of gojuryu as taught to them by Miyagi and therefore are all valid versions of is teachings. I also think that there is much more in common with the different branches, then differences.