Which one (British or American) is better for IELTS exam? What about TOEFL? I'm lerning American, is it essantial to learn British or not?
As a native English-speaker, I have never taken either test. However, your choice may be influenced by what you wish to apply for using the test results afterward.
It is my understanding that the IELTS follows the British system, whereas TOEFL is the prevailing system for Americans. If applying to a university in the UK, take the IELTS; if it is an American school, take the TOEFL. If it is for employment, find out which test your employer prefers.
While the two tests are obviously scored differently, and may be based on different Englishes, there may be an accepted conversion system for the test results whereby one test's results may be reasonably assigned an equivalency for the other (see links below).
You can find an Information for Candidates booklet on the IELTS website.
The international test
IELTS is internationally focused in its content. For example, texts and tasks are sourced from publications from all over the English-speaking world; a range of native-speaker accents (North American, Australian, New Zealand, British etc.) are used in the Listening test; and all standard varieties of English are accepted in test takers’ written and spoken responses.
As such, there should be no problem with using either US English or British English.
The misconception is the British and American are so very different. Of course there are differences, but compared to (say) German or Spanish, the variation in dialects in English is small. If you are learning American English, you are able to understand normal British English speakers. The grammar is almost identical, there are a few vocabulary and spelling differences. The variation in accent is greater within British English, than between British and American.
Both the TOEFL and IELTS people recognise this. And assessors don't discriminate between correct British and correct American English.
Naturally, if you intend to come to the UK, it would make sense to study British English, but that's not for the sake of the test