I have gold/platinum with both carriers but clearly prefer Qatar.
Qatar has cleaner and more modern jets (A350, B787), better business class seats, a much better IES and also less delays. Also Doha Airport is much more convenient.
Qatar has also the far better safety record, also security at IST after the recent attack is an obvious risk.
The only thing I like from Turkish is their Do&Co catering and the IST lounge.
I do not think that otherwise the THY onboard service is better, on all of the many long distance flights I took from Asia the crew always completely disappeared after the meal service and forced all passengers to shut the blinds on a day-flight. Also too often the seats and/or screens in business did not work.