They access different databases, so its worth trying both methods.
I suggest using NAIC first, because they send the request directly to participating insurers who scan their databases. Plus its free.
MIB uses their own database, and not all policies are reported to the MIB. However, MIB could have info on a policy who's insurer does not participate in the NAIC program. But I would think a good many insurers participate in the NAIC program.