The British Council is currently running a free online course about IELTS- the information is very basic, but if you're not familiar with the exam, you would learn a lot.
I think it depends on your preferences and also if you can choose one of them, sometimes we don't have choice we have to do this or that exam.
I had the chance to choose and a took the toefl exam a few months ago. The main reason was the schedule, because I couldn't found a center to take the ielts exam in my city at the time I needed. I found a spot to take the toefl exam when I needed.
After that I found out that I made the right decisio for me.
I prefer American accent instead of British accent. My score on listening was 30/30, I bet I couldn't had equivalent score if it was British accent.
Second I prefer typing rather than writing, this helped me too.
And finally I feel more comfortable talking to a computer than to a examiner.
I know that TOEFL is required if you want to study in America. It's designed to test if you can read academic texts and if you can develop yourself in a university classroom.
I think that IELTS is more general.
I recommend the Cambridge Exams.