As mentioned, cost is one factor. A CT is easier to read, and doesn't need specialized training like a PET, no specialized diet, fasting, so is the most often utilized scsn. I had about 11 PET/CT scans, some costing $6,000. It also depends what the doctor wants to view, area, to indicate which diagnostic test to use, sometimes multiple ones. CT is also good to highlight bone involvement, MRI for vessels, nerve line involvement, and a PET/ CT for distance metastases, and lymph nodes. I also had an MRI's followed by a PET/CT due to tooth filling scatter. I read that the most accurate is the PET/CT, down to as small as 5mm, then the MRI, followed by CT. PET also has a high rate of false positives. Some say it's 90% accurate at 8 weeks, 3 months is the most often taken, 4 months is better, and at a year is 100% accurate. I had most scans done at 3 months, and two at 5 months, 8 months post treatment for various reasons, and that's long waiting.
I'm also have a scheduled for a PET/CT in August, without CT contrast, due to the kidneys. At first my ENT was scheduling a CT, but I needed the nephrologist's clearance, and in between my RO, who specialises in HNC, said I need to get a PET/CT, and that is what I'm having. Personally, I would rather have a PET/CT, and If needed, another test to follow to highlight the area they want to view, as Don mentioned, I don't think it as good in a PET vs stand alone CT.
Good luck with your scan.