The main difference is that 1Password requires two pieces of information for decrypting your passwords while Bitwarden requires only one.

Requiring an additional secret in the form of a decryption key has both upsides and downsides:

• if someone somehow gets access to your master password, they won’t be able to decrypt your passwords unless they also got access to your secret key (or one of your trusted devices)
• a weak master password doesn’t automatically make you vulnerable

• if you lose access to your secret key, your passwords are not recoverable
• additional effort to properly secure your key

So whether you want both or only password protection is a trade-off between the additional protection the key offers and the increased complexity of adequately securing it.     Your proposed scenarios of the master password being brute forced or the servers being hacked and your master password acquired when using Bitwarden are misleading.

Brute forcing the master password is not feasible, unless it is weak (too short, common, or part of a breach). By default, Bitwarden protects against brute force attacks on the password itself using PBKDF2 with 600k iterations. Brute forcing AES-256 (to get into the vault without finding the master password) is not possible according to current knowledge.

Your master password cannot be “acquired” if the Bitwarden servers are hacked.
They store the (encrypted) symmetric key used to decrypt your vault as well as your vault (where all your passwords are stored), AES256-encrypted using said symmetric key.
This symmetric key is itself AES256-encrypted using your master password (this is a simplification) before being sent to their servers.
Neither your master password nor the symmetric key used to decrypt your password vault is recoverable from Bitwarden servers by anyone who doesn’t know your master password and by extension neither are the passwords stored in your encrypted vault.

See bitwarden.com/…/bitwarden-security-white-paper/#o… for details.