Their software does see your master password. It may process it locally, it may not. If it's run in web client inside browser, that may change at any second. This may happen due to attack, their mistake, their dependency vulnerability or plain lie on their part. Fundamentally you need to trust them.
In case of keepass and independent sync(doesn't have to be Dropbox), software that sees master password doesn't need access to the internet. Can be even airgapped if you are extra paranoid.
So to sum it up: keepass + sync is better, because there's no single party that is even able to screw up you to the point of leaking your passwords. "Impossible to fail" is better than "they are doing their best, pinkie promise".
Also - why pay recurring fee for yet another cloud storage, when I just need plain encryption software.
