It sounds like you don't actually understand what these databases are. They are functionally quite different. There are fewer things you can screw up security-wise with a dbm file, but that doesn't mean MySQL is insecure.
I don't know too much about either to be sure, but I do know enough to be able to open, close, read, write, etc. I'm essentially wondering, if I was going to store usernames and passwords, for ease of use and decent security, which would I use?