Consider that with chrome (and chromium based browser) we're close to the situation we had back in the days with IE.
So I'd say open standard definition for web API should come first, later each browser will have their own release process to include them inside but at least behavior and aspect are defined upfront and this will avoid lots of issue
As of today for example and I'm using both Firefox and Chrome daily. You'd be surprised on how many website have been tested only in Chrome and some stuff do not work in Firefox at all