ITA with everything DeeDee said
Our 2e ds has had both private and school evals - here are a couple of other things I'd add to DeeDee's list of things to consider:
* Our school district has very specific guidelines (and rules re #s on test scores etc) that are presented as "bars" to fall under when qualifying a student for an IEP. The intent of IDEA is that eligibility is a team decision and that you need to consider each individual child's needs - but the reality (for us) was that you couldn't open a door to even discussing consideration for certain types of in-school services (such as OT etc) if your child's test scores didn't fall below the cut-off mark or fit a specific set of "guidelines" - yet they might very well be services that would benefit your child tremendously. This is just an example which has nothing to do with your situation, but our ds was extremely challenged with expressive language in elementary school - yet he couldn't qualify for speech therapy because he didn't have an issue with articulation.
* WIth our neuropsych evils we had more freedom to ask and answer questions relative to the diagnosis - which in turn helped us understand better how to help our ds - at home and at school. The recommendations included things we had to do privately (with recommendations for private providers) that the school would not have suggested because ds didn't qualify per their rubric - yet in most cases, they were things that helped ds tremendously and I don't regret having done them.
* With a school eval you are most often looking at a suspected issue and targeting the assessment based on your suspicions of what the issue is. A neuropsych eval starts with a broad look at a child's functioning, then narrows down which tests etc to run from cues based on your parent interview, nueropsych observations, and results from the generic testing. This gives you a chance to potentially uncover issues that aren't all that obvious and that you weren't looking for.
Re the OP's question about the difference between educational testing (private) and a neuropsych - our experience has been that the psychs who are offering services as "educational psychs" usually don't include tests for executive functioning, visual motor integration, behavioral surveys etc. It sounds like the tester you used for your dd may include *some* of that.
Best wishes,
polarbear
