I was interested in this possibility too, but there are only 22 spots available yearly! Very competitive, and most applicants back-up in psychiatry.
The advantage is that instead of being a psychiatrist or neurologist with a neuropsych fellowship, you are actually certified in both. This means you can do both kinds of work, and bill for medical and psychiatric, and be on interdisciplinary teams or managed care panels etc. as a neurologist *and* a psychiatrist.
It's a great opportunity if you really want to work in *both* fields. If you don't care about dual priveleges and just want to be a neurologist who studies/researches behavior, it would probably be much easier to do a fellowship.