First, you are not required to use dropbox with 1Password.
Second, the data stored in dropbox is encrypted by a key that only you have. Dropbox has no way to see what is inside that bundle without your long password.
I've tested just about every password manager because it was up to me to choose the most secure one for my company after we noticed some suspicious activity going on.
There a few products I liked, but I can say unequivocally that Keeper is the best solution for IT folks. It's hands down the most secure and it's the most intuitive for people of all backgrounds.
Keeper generates 256-bit encryption keys using PBKDF2 with HMAC-SHA256 and a minimum of 1,000 rounds, and user data is encrypted with 256-bit AES ciphers. They're a zero knowledge platform, so the cipher keys to encrypt and decrypt user records are not stored or transmitted to the cloud.
Works on every browser and platform, including Linux.
They have all of the standard password management features as well, like autofilling logins, generating random, complex passwords, two-factor auth, fingerprint login, etc... It's made my life a lot easier.
1password is vulnerable to hackers because they rely on third party storage via dropbox. I wouldn't trust my sensitive info with them.