Is distinguishing Hadamard matrices _really_ NP-hard?
Both sources you cite are from the same author. Note the full quote:


  For identifying the equivalence of two Hadamard matrices of order $n$, a complete search compares $(2^n n!)^2$ pairs of matrices and is known to be an NP-hard problem when $n$ increases.


I don't think the author knows what NP-hard entails and confuses it with simply exponential. Further evidence of this is that he states that a complete search (an algorithm) is NP-hard, when that is a property of a problem, not an approach or algorithm.

This source from a different author similarly misuses the term NP-hard:


  The classification of Hadamard matrices of orders $n \geq 32$ is still remains [sic] an open and difficult problem since an algorithmic approach of an exhaustive search is an NP hard problem.


In fact the wording is very similar and found in a field study. It would surprise me if the source of this error wasn't the original paper(s) above being copied without thought.

Since these authors consistently seem to misunderstand the meaning of NP-hard, I think their claims (that come without proof or reference) can be safely dismissed.