This is a tough question and really depends on what you need the test for.
Both are highly respected in many educational institutions and businesses worldwide.
The IELTS is the most widely recognised test and is popular in the UK and across Europe. The TOEFL is sometimes favoured in US institutions, though. If you know where you want to study/work, then the best thing is to ask if they have a preference and go from there.
It is worth noting, though, that despite the IELTS being favoured in the UK, in fact, it was designed by Cambridge English as part of Cambridge University, it has been praised for including a wide variety of accents. Whereas the TOEFL uses American English.
The good news is there isn't much difference in the way you can take the test, though with both now offering the option to take the test from home, online.
The IELTS is considered to feel more natural (the SPEAKING section includes live conversations) and shorter, but the TOEFL has lots of easy-to-answer multiple-choice and short-answer questions.
If you are still not sure, don't worry, we can discuss it together in our first coaching session.