I can't speak to security, but from a functional standpoint the tree and key-value structure of password managers allows easier third party integration into browsers etc, compared to a flat file.
Also you have search and don't expose the other passwords as you would in a textfile. There is pretty good apps for Keepass, which offer a Keepass Keyboard so you don't need to use the clipboard (which can be read by any app on Android for instance).
