Yes, the overall ANOSIM is rather ‘blunt’. I have never run a classification where the resulting PATN-produced groups were not significantly different from random. The test was designed more for a-priori groups.
The pair-wise ANOSIM is doing the same, but limiting itself to taking each pair of defined groups independently from all other groups. If you had two groups, overall and pair-wise should be the same.
The pair-wise test could be used to identify if the number of groups is reasonable. I would however think that PATN generally does such a good job that you would find that you would have to generate many more groups than convenient to get down to a point where discrimination maybe lacking. Personally, two-way tables (and box and whisker plots) will give you a simpler way of understanding the heterogeneity.
So, while pair-wise ANOSIM is focusing on a smaller (simpler) domain, I still think it is somewhat tangential.