A CT scan is the cheapest scan, but most often used, and needs no special training to view, unlike the PET/CT, or diet needed to be followed including the MRI, and unlike a PET/CT scan. Each type of scan show details better than the other Like a CT is good for bone, MRI for nerve, veins, PET/CT for full body, and nodal disease, but are used interchangeably. An MRI may show less scatter, and needed one after a PET/CT to show a more detailed area. For my original diagnosis I had a CT, FNAB, PET/CT, and a triple scope, all which showed cancer suspicion and proved cancer from the biopsies.
As far as being more accurate, specific, sensitive, in detecting cancer I've seen ranges for the PET/CT scan, 90% range, then an MRI, high 80% followed by the CT scan, in the 70% range, but again, this depends on the area scanned in the body, and what they are looking for, other involvement, type of cancer.