Postdoc Prestige

Question from a reader:
In your experience in faculty search committees, with respect to hiring an assistant professor, are postdoc positions at national laboratories (e.g. Sandia) viewed with higher regard, equal regard, or lower regard when compared with a postdoc at Prestigious University?
In my experience, all other things being equal (even though they never are), these postdocs would be held in equal regard. I say that mostly because national lab postdocs are certainly not held in lower regard, and I can't think of why they would be held in higher regard.