Obviously, neither version is "more correct" than the other. I cannot penalise a student for writing "color" instead of "colour", or "cellphone" instead of "mobile phone" -- all these terms are perfectly correct English, they're just slightly different varieties of English.
And when we add other varieties into the mix, it gets even more confusing. Canadian English, for example, traditionally uses British spellings, but since Canada is so close the United States, American spellings are becoming more common and accepted; and Canadian English is more like American English than British English.
In German schools, the usual guideline for teachers is this: If a student writes a text in American English but slips in an anglicism or a British spelling, it is underlined and marked "BE", but not counted as an error; if a student writes a text in British English but slips in an americanism or an American spelling, it is underlined and marked "AE", but not counted as an error.
That seems fair to me: the students aren't being penalised because they're actually writing correct English; but they are alerted to the fact that it would be counted as a mistake in the US or the UK.
There are few cases where the pronunciation is so different that it matters. If it does, I just point out that the British or the Americans (whichever is appropriate) pronounce it differently. Since most British people are very familiar with American accents (from movies and TV shows), and Americans are now becoming more familiar with British accents, it's not as big a problem as it was 100 years ago.
I do remember once case where I was penalised for using the wrong pronunciation. At primary school level, we were regularly tested on our reading: we had to read out a series of words printed on a card which got more and more difficult, and depending on how far we got before we made a certain number of mistakes in a row (I think four), this indicated our "reading age".
Well, on this one occasion, one of the words I was given was "genuine". I knew what it meant, but I had never heard it until, coincidentally, the night before -- on an American cartoon TV series (Scooby Doo, as I recall). So that's how I pronounced it -- the American way. And I saw the teacher mark it as wrong.
It didn't affect my "reading age", but I've never forgotten it. I thought it was terribly unfair.