Quick answer:
CTs are for looking a bony structures. MRIs are for looking at soft tissues.
A CT is merely a series of x-rays which software then uses to produce a series of 2-D films.
A MRI excites hydrogen atoms which then vibrate and gives off signals which are detected. The more hydrogen a tissue has, the bigger the signal. Since some tissues have more water in them, so you can differentiate it from other types of soft tissues. Soft tissue is anything which isn’t bone.
Some insiders have told me that no one really knows what the long term effects of MRI is since it hasn’t been that long since MRIs were commonly used. The strength of the magnetic field is extremely strong, stronger than can be found in nature. I’m wary of MRIs myself, at least the side effects of CTs (x-rays) are known. There has been a recent study done showing that the effects of many x-rays were not as bad as they thought.
I don’t know why the neurodoc would be using CTs unless it was for cost or expediency. About 7 years ago, the joke amongst doctors was that the only reason why you gave a patient a CT was because an MRI was unavailable.