Arguing about which is better British or American English is like two brothers arguing about whose father is stronger. American English is a variety of British English! The same is true of English in Canada, Australia and New Zealand. These countries were all settled by people from Britain. Other immigrants assimilated to the local variety of English. (The very small remnants of the native populations and unassimilated immigrants add only a little to the national culture.)
American English comes from Early Modern English (the English of Shakespeare) and not modern British English. The modern British English variety most closely related to American English is Estuary English. Estuary English is spoken in London, the Thames river area and South Eastern England. (Although Cockneys would proudly assert that theirs is the real London dialect, Estuary English is dominant.)
Some older English words are preserved in America. Expressions that the British call "Americanisms" sometimes are originally British expressions that were preserved in the American colonies and dropped in Britain. The American word diaper was used in Britain for 500 years. However today, the British use the word nappy. It was first used in 1927. The Americans preserve the Old English form gotten, rather than the modern British form got.
The American practice of using the word fall for autumn came from Shakespeare's time and was short for fall of the leaf (1540s). The harvest was the original English name for the season. Later it was replaced by autumn, which is from Old French. Before Shakespeare's time, farmers spoke English and the colonial aristocracy spoke French. With the change of power, English-speaking people preferred a non-farming name for the season. Two replacement words were chosen but UK and US English used different ones.
The words trash and rubbish are both about 600 years old. Both countries use both words for household waste. Although today the British prefer to use rubbish at a rate of 10 to 1. The Americans tend to use trash, instead of rubbish, in the same ratio. Neither use is much older than the other.
The Americans have the same ancestors as people in the UK. The differences between English in London and English in New Zealand are smaller than the differences between London's English and that of some other parts of the UK. Compare these native speakers to second-language speakers. For example, in both Hong Kong and India, English is learned at school as a second language. The British colonists have left, been assimilated or marginalized as a minority. From a global perspective the Americans and the British have the same language.