The IELTS test is administrated by the British Councils, the University of Cambridge, and IELTS Australia.
That is to say, it is associated with the British government and traditionally was used by British universities, as well as New Zealand and Australian universities to determine the language capability of foreign students.
TOEFL is administered by ETS, a US-based non-profit and is used widely by American and Canadian universities. However, these days, in order to make it easy on international students, universities all over the world take both TOEFL and IELTS.
While you should check with the specific university you want to apply to, in general any school in the US, the UK, Australia or New Zealand will take either test score. So that's one worry off your mind. Pick the test you think will be easier for you to complete. To do that, you probably need to know the structure of each exam.
Check the following links : http://www.ets.org/toefl/ibt/about/content/