Honestly that statement sounds like BS to me. Also, this person is trusting his life to a third party as well: the browser vendors’ cryptography implementation.

I think for an average person, the biggest factor is not the strength of the security. You’re already better than 99% of people if you use different passwords per site and store them behind a password. No hacker will spend weeks cracking your passwords if he can get the passwords of those other 99% for free.

So I’d say, pick the solution most convenient for you that is least likely to break over time. And an established name like 1Password sounds great for that.