I work with APIs all the time and I work with web developers who insist that OAuth, OpenID, etc are far superior than a homebrew method. Every site seems to be using these as well now for ease of use to the user, but also for security. I hear it every day almost that it's more secure, but I find that extremely hard to believe for a few reasons:
If a hacker somehow gets your password to one site, he know has access to the majority of the sites you visit now.
It makes phishing 10x easier. With so many people using the same logins and doing it over, and over again people are less likely to actually read everything and check the URL up top.
Could you list of more reasons why it's unsafe or could you explain to me why it is more safe? I don't see why you would put up with the hassle of integrating one of these when it seems like a user would be fine entering in 3 fields (username, password, email) instead of clicking service logo to login (Twitter, Google, FB etc), entering in their username/password, clicking submit, clicking approve.