I'm mostly wondering about vocabulary (e.g. truck vs. lorry; apartment vs. flat) but I suppose I'd be interested to learn about pronunciation too. Intuitively I feel like this could go either way. On the one hand, all languages drift and given enough time, this drift should draw the two further apart simply by chance.
On the other hand, mass media and internet give us more opportunities to communicate with each other than ever before, and pick up pieces of each other's vocabulary. For instance, the Northern Californian "hella" appears in British English, despite having only arrisen in the past 20 years. The British "fish and chips" appear in American English despite having only arisen in the past 150 years.
So are these two dialects more or less alike than they were 10 years ago? What about 30 years ago? 100 years?