Well something is weird there because the only table we need to look at is posts. Technically the size should be identical if you converted the post content byte-by-byte.
Maybe miniBB was storing as single character ascii and bbPress is storing as double character UTF8? That would explain it. bbPress is exactly double the size because it's using 2-byte encoding of the characters.
I know it's bothersome but 8MB is trivial these days.
In theory you could force bbpress to change character sets to your old type and force phpmyadmin to convert the table. But many things could go very wrong with that.
Another thought might be index size?
If you go into each table it will tell you the data vs index size.
Take a look at the index size for bb_posts vs minibbtable_posts
If you are willing, I am curious to see a screenshot of those two also.