> I'm not aware of any meaningful differences between using the browser's password vault vs. using a local password manager's vault.Both are better than using the same password, or overly simple passwords, on multiple accounts, and other human flaws. Beyond that there are some subtleties in the threat models, so the two options have a couple of slightly different risks.
If your browser is hacked, passwords stored in it could be unsafe. While the browser makers take great efforts to properly segregate the functions to reduce the risk, there have been cases where malicious code has been able to circumvent those efforts through bugs to gain access. There is also the issue of local attacks: if someone manages to unlock your workstation (or you accidentally leave it unlocked) your browser may helpfully fill in passwords where an external vault would not (or course if you left that unlocked too, this difference is moot).
Likewise the external password manager often means credentials being carried over the clipboard, and if not that then the OS message queue. Both of these can potentially be intercepted by any malicious running code that has managed to get into your current session, or you could simply cock-up and paste them into the wrong place (or perhaps have the password manager send them to the wrong place due to confusion over which window will get input focus when the password manager starts sending messages).
Personally I go with the external app and refuse to store passwords in the browser, in part because I like having to actively switch to it, unlock it, etc, because the possibility of more automated features (even if they are optional) makes me feel less safe. But there are safety arguments both ways, and for most people the distinction is not important: in both cases if malicious persons or code are that close to your credentials, in either storage location, you are probably rather screwed anyway!