For Watson Speech to Text - Did you choose the correct model to match your source audio quality? They default to a "Broadband" model intended for high quality audio sources, but you can also select "Narrowband" for things like phone quality. Not guaranteeing a difference, but in my experience, matching the source quality to the correct model makes some difference.

I've not compared them extensively but for streaming realtime, I found that Watson beat the Google api for a specific use-case. Your mileage may vary!

They also provide a handy Mic / File reader interface for browsers: https://github.com/watson-developer-cloud/speech-javascript-...