From the perspective of a British person, I'd say that contrary to the assurances of many folk here, they are not technically both correct. Or rather, whether they are both correct or not depends on context.
It seems that both spellings are acceptable in the US, but here in Britain it would certainly be viewed as incorrect to use the American spelling. I'd have been marked down for it in my dissertation last year, I can assure you. Exceptions are likely made if you are an American living in Britain, but a British person living here would be expected to use British English.
This is likely because American English was adapted from the British version. Over there, the British version is just the archaic spelling of the current standard American version. The British spellings were once part of the language, even if they're not used anymore, so it isn't incorrect to use either the old or new version. However, for British people... the American versions have never been a part of our language. We have never used them. They're just misspellings.
So whether they are correct or incorrect depends on who and where you are.
This perhaps also explains why a lot of British people view the American versions as bastardisations of "true" English. They are mutations of the original language separate to the original language... They feel almost like flaws caused by erroneous printing, like those famously present in the Lord of the Rings and such. Errors that gained popularity and became widespread; mistakes that were propagated instead of corrected and somehow accidentally became convention. Personally, I absolutely loathe the American way of spelling most words where there's a difference. It always seems stylistically crass.
Of course, I'm not an obnoxious cunt, so I don't criticise people for using those spellings when that's the way they were taught to spell them and when I know that for them it's a perfectly legitimate way of spelling it... but I can totally understand why other people feel they're incorrect. It seems stupid to make a fuss about it unless actually asked, though.