# Naive Bayes vs Full Bayes model classifiers

I have a hard time to understand when Naive Bayes works better than Full Bayes.
In general, i know that naive bayes does the assumption that features are independent given the class.
However, if features indeed independent, does it mean that assuming that they are dependent yield worst result?

e.g. i got this data points for two features, each class is colored in different color.

Now my intuition is that Naive bayes will work well here, given a specific class we have two different distributions of the class and both are "unstructured".
However, i did ran Naive bayes (with normal pdf) and full bayes (with multivariate pdf) classifiers on that data (using multivariate) and got the same accuracy.