Firstly, it wasn't just Brits in either Australia or America (in fact in great swathes of America the language of choice was French, German, Irish, Chinese, Swedish, Spanish or Dutch). InAustralia - although it was a British colony there were loads of Irish and other Europeans. In both cases you're hearing what's the result of several hundred years of integration, all the accents mixing into what you now hear.
To be honest, I think it's even more interesting that there are so many dialects and accents in a small island like Britain