They're very different specialties, as has already been stated.
First of all, the route to each is completely different after medical school. Neurologists do a medicine internship for a year, and then three years of neurology residency. Neurosurgeons do a surgery internship for a year and then 5-6 years of neurosurgery residency.
Their typical days are also completely different. A neurosurgeon's typical day starts between 5-6am with brief rounds on the patients: basically, are they still alive, and if so, is their basic neuro exam improving or worsening, are there any active general medical problems (for which medicine will be consulted), and what needs to be done that day? +/- breakfast, then to the OR from 7:30am till all the cases are done for the day, which can be anywhere from noon to midnight or later. While you're in the OR, patient care is handled by the junior residents or PA's. Attendings will operate on certain days of the week, and have clinic on the remaining days. Residents generally follow the above schedule every day, with perhaps one half-day devoted to clinic, a full day if you're a junior.
In the academic setting, a neurologist's typical day starts at 7-8am with rounds, which extend until noon or later. Patients are presented and discussed fully, as are all their treatment options. Particular attention is paid to localizing the patient's lesion, and it's a point of pride among neurologists to know the answer before seeing the scans. Neuro exams tend to be more detailed, and the neuro team will handle many of the less complicated medical problems themselves, mainly consulting the medicine subspecialties for complicated problems. At some point in the morning, neuroradiology rounds take place, where all the MRIs and CTs are examined with the radiologist. Afternoons are devoted to clinic, and the day ends sometime between 4 and 6pm.
Their approach to patients is also very different. Neurosurgeons lose interest quickly if the patient's problem is not amenable to surgery. They will follow a patient only as long as there is a problem potentially needing surgery, or post-operatively until all problems associated with the surgery have resolved to the extent that they ever will.
Neurologists, on the other hand, generally continue to follow their patients from the point of referral onward until the patient dies or changes doctors.
The bottom line is not so much whether your interest is in neuroscience, but rather whether you prefer surgery to medicine. Answer that question first, and the rest will be easy.
During my Neuro rotation, I was always frustrated to spend hours on 1 patient trying to localize the lesion when the CT results were in the computer already waiting for us. I guess I have the surgeon mentality. 😉
