Language teachers all over the world today are wondering about this very question. Each country wants to promote its own variant of English throughout the world. I was born in London that's why I've been teaching British English for twenty years already. But it's more than my birthplace that makes me do it. I consider British English the only correct version of English. Besides, British English has a longer history than American English. After all, American English developed from British English and has only a short 200-year history. I know that now, as students in Europe choose a second language to study, the choice is often American English, full of abbreviations, slangs and twangs. I would recommend young people to learn British English. They won't regret choosing British English, "the Queen's English" as we call it. And British teachers will do their best to keep and promote the purest form of English, which shouldn't be changed.
To some extent that depends on who is doing the teaching. After all, a British-born teacher will naturally teach the British variant and vice versa. But I think American English is winning and I guess it probably should be. It's much less rigid than British English. It's a more lively and flexible language, open to change. Young people everywhere choose American English without question and regret. There are some strong reasons. The most popular reason has to do with travel. When I teach bright youngsters and we talk about travel they all want to go to the United States, regardless of where they're from. For them it's a passport to jobs and money as well as pop culture. America's colourful pop culture is another strong reason why many learners prefer the American variant. All language learning is related to culture. For all its faults American culture just happens to be widely popular at the moment. It's much more exciting.