OpenID fundamentally argued that you should trust a third-party authentication service. Not too long ago, Mozilla tried implementing OpenID directly in the browser so you didn't have to trust any third party, but that represented an afterthought in the OpenID ecosystem.

BrowserID, on the other hand, fundamentally uses distributed identity via public/private key crypto, and only involves a (single) third-party service as a crutch to allow browsers without native BrowserID support to handle BrowserID, so that sites can adopt this immediately rather than waiting for browser support.