neurology and psychiatry are totally different fields. the idea behind combined neuro/psych residencies had been that the fields were converging and as such there was need for the dually trained practitioner. this turned out to be completely false, and most of these programs are dead or dying. there are very few spots for combined neurology and psych residencies, although sometimes programs have created this. given how much there is to master in one field alone, and the trend is towards create specialists and not generalists, it is not really possible to practice in both neurology and psychiatry with a broad practice. also in the combined programs something has to go (it is 6 years - 2.5 years of neurology and psychiatry each after a medicine internship) and that is psychotherapy. being able to think psychologically about patients, and understanding the principles and practice of psychotherapy is one of the key features of psychiatry, even for those who do not want to do therapy themselves. this is not something you can get much experience in with combined programs. most neurologists are comfortable starting antipsychotics or antidepressants in patients with neuropsychiatric symptoms, what they lack is the psychological knowledge in formulation and therapy so it is unclear how these combined programs will help in this regard.
It is possible to do cognitive/behavioral neurology fellowships after neurology training. These particular focus on dementias, but also other neuropsychiatric symptoms following stroke, trauma, genetic, neurodegenerative diseases etc - e.g. depression, apathy, psychosis, amnesia, agnosia, apraxia, disinhibition. It is also possible to do an fellowship in neuropsychiatry following psychiatry residency (which may be the same fellowship as above). Again these tend to focus on Alzheimer's but also other emotional, cognitive and behavioral sequela of neurological disease. There is neurological presentations of psychological disorder (e.g. conversion disorder).
Neuropsychiatry is an academic specialty, so almost everyone practicing in the field works in an academic center, and does research etc. If you have lofty ideas about being the next Oliver Sacks, you can think again. Much of neuropsychiatry is fairly garden variety but there certainly are some very interesting cases, though often little in the way of successful treatment. Bearing in mind that Oliver Sacks actually loses >$20 000/yr from seeing patients, having a niche neuropsychiatric practice outside of academia is not really financially viable.
Neuro vs Psych comes down to what do you want to treat? headaches and stroke vs schizophrenia and depression? Do you like doing procedures vs talking to patients? Do you care (or can you pretend to care) about the peripheral nervous system? How do you feel about working with severe personality disorders and addiction?
