I will have my car serviced tomorrow sounds fine. I talking to most people, i would say, I’m going to have my car serviced tomorrow. More casual. Serviced is also maybe a bit of an odd word, for American usage anyway.

For casual use, they are equivalent in North American English. For English exams, they are not. If you have the excellent book English Grammar in Use by Raymond Murphy, consult Units 19-22. 19 - Simple present and simple present continuous for scheduled future events. “I’m having my car serviced tomorrow.” 20 - Going to + verb for planned events. “I’m going to have my car serviced tomorrow.” 21 - Simple future for decisions. “I will have my car serviced tomorrow.” Here is a useful summary of different ways to express events in the future: www.ef.com/ca/english-resources/english-grammar/future