From reading about it, Noire de Babentane and Bourjasotte Noire are closely related. They are different as follows.
NDB ripens two weeks earlier than the Bourjasotte Noire.
Better performance in humid conditions.
It has smaller and slightly lighter fruit than the Bourjasotte Noire,
The shape of the fruit is slightly flattened vs a perfectly cylindrical Bourjasotte Noire.
As far as flavor is concerned it is subjective.
Leon, Does your Noire de Barbentane form a honey drop when ripe?