You log in every day to LastPass, giving them a lot more opportunity to intercept your password without changing anything on the client side. LastPass also has a web interface where you can log in, and you often need to log in there in order to make changes to your account. This can act as an additional attack vector if they were compromised.
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.
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.