MRIs use magnets to image, CTs use radiation.
MRIs do a better job on soft tissues, CTs better at bone (so ears and structures)
MRIs can show you on two views (or more), CTs can not.
CT's are also significantly more dangerous.
If a dye contrast medium is ingested the medium used with the MRI's is also less hazardous that that used with the CT's.
If you are in a severe accident and need imaging and only a CT is available, then it becomes acceptable risk with great benefit.
Otherwise the MRI wins hands down.
In addition MRI's are classified as to the tesla power of the machine.
Most MRI machines in use are rated at 1 T (or Tesla).
A 3 T (Tesla) MRI machine can do anything a CT can do better.
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A CT scan gives a more clear picture of bone structures and less clear picture of soft tissues. The vice versa is true for MRI. MRI can produce images in any plane but CT scan cannot. CT scan uses X-ray imaging whereas MRI uses radio waves and magnets. Radiation exposure is moderate in CT scan and there is no radiation exposure in MRI.
Hope this helps. Please let me know if there is any thing else. Take care!