BrowserID has other advantages over OpenID. It has a big privacy advantage: with OpenID, your OpenID provider is informed of every site you log into, every time you log into it. It's like the government being informed every time you present your driver's license as ID. (Actually worse, since the ID provider can selectively deny authentication on a site by site basis.)
With BrowserID an ID provider can at most deduce (via its key being fetched) that *some* unspecified user is logging into a particular site, and because the key is cached this notification only happens once in a while (e.g. every 12 hours).