Neurosurgeons are probably better at the exposure.
Orthopods are better at dealing with bone obviously, so they probably have an edge in achieving stability and fusions with instrumentation.
Which is what I have seen at some hospitals the neurosurgeon does the exposure and the orthopod comes in and does the instrumentation.
This is NOT the norm for sure. The surgical approach to the spine is easy for the vast majority of spine cases, so there's not need to have an "approach surgeon" unless you're doing an anterolateral or anterior approach where a vascular or general surgeon would be helpful (although there are neurosurgeons and orthopedic spine surgeons who sometimes do those approaches by themselves -- not something I would recommend, though).
The debate here is simple and someone else on the thread already mentioned it. Choose your surgeon, not their specialty. Orthopedic spine surgeons cannot go intradural, whereas neurosurgeons can go anywhere in the spine. Orthopedic spine surgeons also don't general deal with the craniovertebral junction, but, on the other hand, they are may be more comfortable dealing with low sacral/pelvic pathology. More orthopedic spine surgeons seem to get into scoliosis surgery/major deformity work, whereas most neurosurgeons do not (mainly because it requires a humongous referral base and it's painful surgery, and neurosurgeons are busy with the rest of their neurosurgery practice).
The other factor I would consider, and I hope I'm not offending any orthopedic surgeons out there, is that orthopedic surgeons have a reputation of being good technicians, but terrible doctors…meaning, they don't know how to truly take care of a sick patient. Neurosurgeons, on the other hand, are intensivists by training and the specialty board exam they pass qualifies them to be intensivists. A lot of their training involves sick patients, and they are generally very skilled at taking care of sick patients.
And FINALLY, I would say that orthopedic surgeons and neurosurgeons often work together and consult each other, so the spine world is truly a mixed bag with much more collegiality and crossover of training methods and skills than ever before. For example, neurosurgeons are training orthopedic spine surgeons and orthopedic spine surgeons are training neurosurgeons in fellowships and residency programs across the country.