MRI is generally more effective at seeing the different types of soft tissue, CT uses x rays which aren't so good. But contrast can be used so that the inside of the bowel shows up clearly on either ty of scan.
MRIs have no radiation, so are useful when patients need repeated scans.
MRIs cannot be used if the patient has metal in their body, as it uses an extremely stong magnetic field.
I think MRIs are newer, therefore less readily available (longer waiting times) and more expensive.