Yes, there is:)

Wald tests/CIs are crude approximations. They were invented in times where is was too demanding to actually calculate the likelihood profile. The profile-likelihood test/CIs are better approximations.

Rule: If available at similar cost, use the better approximation.

NB: multivariate means more than one DV and hence multivariate and binary are mutually exclusive. Best, D. Booth

David Eugene Booth, couldn't it be that multiple binary DVs are meant?

@Jochen, Sure but in case you don't say so you have confused the reader. i am often confused on this point in reading these questions. Improvement in exposition(including my own) would be helpful. Best wishes, David