The two sentences mean the same thing. There are several ways we can form negatives in English, including:
Using the adverb "not".
Using the adverb "never".
Using the adjective "no".
Using a pronoun such as "none", "no one", or "neither".
Your sentences 1A and 1B are very similar, except that the positive equivalent of "never" is "ever", so sentence 1A could be "I haven't ever eaten sushi before."
I wouldn't include "ever" in sentence 2A, though, because it was included in the question. The biggest difference that I can identify in sentences 2A / 2B is that when speaking, you could place emphasis on the negative word "never"; you can't stress the clitic "n't" in sentence 2A.