Is it possible/appropriate to compare two or more F-statistics results, say from an ANOVA or MANOVA, to say which analysis has a larger difference when both p-values are the same(and sig)?

Is it possible/appropriate to compare two or more F-statistics results, say from an ANOVA or MANOVA, to say which analysis has a larger difference when both p-values are the same(and sig)?

When doing a MANOVA, you want to consider which omnibus test might be best for your situation. It's possible one or more is most ideal based on it's performance characteristics, so you would look at the one/few you preselected. Do some research on when to use Pillai's trace vs Wilk's Lambda and so on and see which is best for your scenario.