Bonferroni count = 1 in GO-Slim overrepresentation test (PANTHER) is it possible?
GO-Slim BP, Binomial, Bonferroni

This seems easy you because I suspect have run too many tests at 5%.
If you run 10 tests at 5% rejection threshold, the Bonferroni correction threshold is 0.5% - you divide the number of tests by the rejection threshold.
One possibility is the rejection threshold is given in number of genems: in one instance you've run a pairwise test with several thousand genes so the rejection threshold has been set accordingly. The other test you ran I suspect was a multi-variate test, thus the shift in rejection threshold measured in number of genes.

The altnative is that Bonf = 1 is in fact P = 1, in other words there is no significant difference at all.  If P = 1 then this could be no genes show deviation hence 1770, because 1770/1770 =1
Looking at it again the above seems a better explanation.