I would also say that it also depends a bit on if you have a neurosurgery department in your medical school. Private practice folks will be okay for research, but it definitely will require you to do more away rotations (at least three) if you don't have a home institution to write you a chairman/program director letter. Neurosurgeons only care about letters from other neurosurgeons, but those in private practice may not be well recognized enough to bear as much weight except perhaps at the program where they trained.