The main benefit is being able to access passwords without using a web browser.

For example, say you need to tell someone your credit card over the phone. With Safari you need to go into Settings > Auto Fill > Edit > unlock, and finally you need to click on the card number to view it. That's a horrible process.

With 1Password I can hit a global hotkey, you might use control-space for example, type 'card' and there it is. 1Password even has hotkeys to quickly copy the name/number/expiry/security code with a single key press (for each one).

Another big advantage is most password managers have OTP support. Safari and Chrome do not.