Pros:
- you don't have to store/transfer the encrypted vault (usually few kB in size)
Cons:
- can't rotate passwords if service needs you to change it (leak, periodic rotation etc.)
- it can't support two factor auth (for the manager itself)
- it does not support auto-fill (but theoretically can, through a browser extension)
- it's web only (harder to trust)
- if one of your passwords leak, it's as if your whole password vault leaked -- the attacker can just brute force "master passwords" until they arrive at the same password, after which they can generate all of your other passwords