what separates the U.S. from Britain linguistically?

[ilikeverin]

A lot of the features of the "British" accent only emerged after we won our independence, iirc.

This.  Many visitors to the "early" US (1700s, early 1800s) from the UK mention how they find the speech of colonial America to be pleasantly "refined" and "proper", because the features we now stereotype as "British" and therefore refined and proper were new introductions to varieties of English spoken in the British Isles and were thus seen as annoying.

Thankfully with mass media, everybody is (slowly) converging.  We might still be speaking slightly different in 200 years, but we might not be.

False.  Mass media is not accelerating linguistic convergence.  Regional dialects may be getting somewhat less apparent in the UK, but that's largely a result of increased geographic mobility.  Meanwhile, dialects are becoming increasingly more distinct in the US, by and large, with the continued decrease in speakers of some East Coast dialects (e.g., Charleston) being more than balanced by large changes in the Rust Belt and California.

[ilikeverin]

A lot of American 'dialects' aren't really much more than accents, though.

Eh, there's no commonly accepted definition for such words.  The most frequently used ones are that accents are what non-native speakers of a language have and dialects are what native speakers have.

False.  Mass media is not accelerating linguistic convergence.  Regional dialects may be getting somewhat less apparent in the UK, but that's largely a result of increased geographic mobility.  Meanwhile, dialects are becoming increasingly more distinct in the US, by and large, with the continued decrease in speakers of some East Coast dialects (e.g., Charleston) being more than balanced by large changes in the Rust Belt and California.

I was under the impression that TV (and to a lesser extent, films) desire to have most "normal" characters speak with a flat, midwestern accent was having a rather large impact on our "lesser" accents.  Hence why people in California and the Rust Belt now sound like they just got off the bus from Des Moines.

Accents in the western part of the country are just less distinct because those areas are more recently settled and have fewer natives.

And California's trying to catch up! (although I don't know about how true the latter representation is... but I've heard Californians speak of it appreciatively)