And if I think about "What is harder for hackers to get to: My encrypted password file on Dropbox or my encrypted passwords on LastPass," I feel I'll have more confidence in LastPass.
Anything very obviously wrong with this thinking?
If 1Password was compromised, on the other hand, they'd have to wait until you upgrade the client to the bugged version. As far as I can tell, they don't even have a web interface for you to log in.
Dropbox doesn't even come into the equation since it's just dumb storage. Someone who compromises Dropbox will only see a useless blob. The attacker would have to compromise both 1Password and Dropbox, as well as get you to install a compromised 1Password client, in order to get your encrypted passwords.
The problem is not open-source/closed-source so much as it is that convenient, centralized, web-based crypto tools are virtually never safe, and that's the problem LastPass has chosen to try to crack.
With 1Password+Dropbox, Dropbox doesn't know your master password. It only ever sees the encrypted vault, and doesn't have any opportunity to intercept any plaintext. (If your password is strong enough, you could probably even get away with posting your vault on a public website.)