Yes, 1Password is closed source. But as far as their security design goes, they are as open as possible. In fact, I recently started looking into https://1password.com/files/1Password%20for%20Teams%20White%... to understand what choices they've made. While I don't have an overview yet, one thing for sure: their key derivation algorithm isn't built for hardware from the past century.

Storing your password database on someone else's computer might not be a bad thing if it is securely encrypted. In the end, most people have more than one device these days. If your solution is doing manual "synchronization" then the result will often turn out less secure.