Do most neurologists end up pursuing a fellowship? If so, why is it so much more attractive than general neurology? What can a subspecialist do that a general neurologist can't?
I have no idea what absolute numbers show, but anecdotally, the majority of neurologists go into fellowships. When I was in residency, I recall that the most commonly selected fellowship was clinical neurophysiology.
Why do so many of us do fellowship? Well, it's multifactorial. I had a personality that drove me toward super-subspecialization from the first year of medical school. The more subspecialized I got, the more I liked it. Fellowship was a way to formally do this for me. So that's one reason.
Also, general neurology is extremely broad, and it's difficult to cover all of your bases in a three year residency. Most of us admit that there are certain areas that we are less comfortable in than others (MS and movement disorders are examples of two common areas of neurology that non-fellowship trained people may feel a bit inadequate dabbling in after residency). Completing a fellowship allows one to learn certain areas that you may have felt deficient in, better learn subject matter you already like but wanted to dedicate more time to, or even to prepare for an academic or private practice career. Most academic programs expect fellowship training at a minimum unless you are going to be a neurohospitalist or run a general neurology clinic etc.
Subspecialists offer exactly what you would think they offer. Namely, more expertise in the far reaches of the specialty that hopefully complement some academic or private practice group. Certain fellowships allow you particular ability to bill for particular procedures. For instance, to interpret sleep studies (and bill for them) for an accredited sleep lab, you need to have completed a fellowship in sleep medicine. Other areas of neurology, such as EEG and EMG, are billable just by viture of completing a residency in neurology.
This is a very broad question. You should research neurology at your home institution and observe what the various fellowship-trained people offer to your program and then proceed to learning more about the fellowships that interest you in particular.