Honestly, it depends on the psych you have. Some SPs can generate an eval just as good as or better than a neuropsych (some actually have post-doctoral certification as school neuropsychs, too).
In reality, the assessment training received by doctoral-level school psychs, neuropsychs, and clinical psychs is very similar, and probably varies more by graduate training program than by specialization. Neuropsychs have a little more neuroanatomy and cognitive science in their basic science education, and an additional course that focuses on tests like the Delis-Kaplan, WCST, and pegboard--but some SPs and CPs have that course, too. Clinical psychs spend a little more time on psychopath--but again, some SPs and NPs may, as well. I've already mentioned that SPs tend to be stronger in school, systems, and behavior--but a CP or NP could choose electives in those areas during their training or later.
I think if you are looking at an outside eval, in response to a recalcitrant district or poorly-conducted school eval, there is definitely value in going to a neuropsych, partly because of the name impact it has on the school system. On the average, neuropsychs are more likely to have certain (very expensive) instruments available, due to the kind of referral questions people bring to them, like the TOVA, IVA, or CCPT. There is no professional or ethical reason a SP or CP could not validly administer and interpret these, but their typical clientele are less likely to require them, so it's not as cost-effective to purchase them.
A CP is the most likely of the three to have access to a Rorschach, so if that kind of perception, ego structure, and reality testing is what you're looking for, then that would be the place to go.
SPs are more likely than the other two to seek collaborative solutions with families and school systems, and less likely to place the onus of disability on the individual child. Recommendations are more likely to consider the ecology of the school, and to be communicated in the language of school culture, thus being more readily accepted by school personnel. So if that's what you need, then take that into the decision-making process as well.
Bottom line, you need to have a good conversation with the psych before signing on. Ask for references, what school systems they've worked with, what a sample battery of assessments would be, based on the referral question, what they would do if an unexpected result came up in the standard battery, who their audience is when they are writing recommendations, their experience with the clinical population most likely in question, how they establish rapport with whatever type of difficult-to-draw-out child you have, etc. Don't be afraid to ask detailed questions. You are representing the client (your child). And -please- allow any evaluator access to prior testing history, to avoid invalidating thousands of dollars worth of testing by re-administering something that has been given recently!
