IELTS or TOEFL iBT?
Depending on your needs, please kindly check what kind of test is required for your program.
However, if both of them are acceptable. I would be considering these things:
The pandemic
You can take TOEFL iBT Home Edition if you aren't comfortable with face-to-face meetings. But based on my experience taking IETLS in IALF Jakarta, they implement the health protocol very strictly, even in the speaking section you'll still need to wear a mask, sometimes I worried that the examiners misheard me. Latest info: IELTS provides online delivery, but I'm not sure about the details.
British vs American
TOEFL are american-based test while IELTS is british-based. Which accent you're comfortable with? Which country are you applying for?
What kind of speaking mediums are you more comfortable with? —> talk directly vs sending recorded voices
In IELTS you'll talk directly, face to face, with the examiners. In TOEFL iBT Home Edition, you'll get the chance to record it instead. It's sometimes convenient however you'll need to prepare a good microphone (you can't use headphone/headset/earphone) if you don't want the examiners to mishear what you spell. Your time to speak will also be limited. Your score will also be assessed via AI. https://www.ets.org/toefl/test-takers/ibt/about/content/speaking/
Computer vs Paper
IELTS has 2 choices, computer-based or paper-based. The computer-based result can be obtained faster than paper-based (3-5 days) TOEFL iBT has 2 choices, computer or paper. However, the computer-based are common while paper-based only available in some countries (6-10 days)
The Schedule
I decided which one to choose based on the schedule. So back then, IELTS had more options than TOEFL iBT on the place. Hence, IELTS was way more flexible for me. But you can choose TOEFL iBT if you want to be even more flexible.
Result Delivery Day
Every institution may give different days for the result to be delivered. Mostly IELTS computer-based results can be obtained in 3-5 days, while paper-based in 13 days. TOEFL iBT computer and home edition in 6-10 days (someone said 6 days for in-place test, while home edition in 10 days), while paper-based in 11 days.
Price
There isn't much difference
No fixed number.