Considering MySQL supports BDB tables, BDB is basically a subset of MySQL, for the most part. I.e. the advantage is that MySQL provides a nice, since to use SQL front end to the BDB tables instead of the library interface most of are used to using.
Probably a bit faster too, due to things like caching and all going on in MySQL, and the fact that MySQL likely is using myisam tables, not BDB when running underneath it.
Of course, BDB would be more reliable in a crash, so there's the trade off.
I wonder if you could make MySQL use BDB or innodb table types for it?