Though these dump utilities don't offer any particular ordering, in general, given the same versions & switches etc. they will produce the same ordering for the same source material. Ie. They don't have a random component.

Whilst it is possible that two DBs that were arrived at via different routes -- ie. a different sequencing of inserts, updates and deletes -- may produce subtly different dumps due to that ordering, that the OP might decide to consider as "identical", it will require a decision to consider them so.

That is, whilst diff'ing the dumps may produce "false negatives", it will require a human's decision to make the determination that they are indeed false.

There is also the possibility to post process the dumps to achieve some 'canonical' format -- eg. trim whitespace; sort etc. -- but that should rarely be necessary.

For the purposes of checking refactoring, it is safe to assume that the OP would be targeting the same versions of the DBMS & utility for both the reference and check dumps; and any variations between them will be of interest, even if ultimately dismissed as irrelevant.