As adjectives the difference between incommensurable and incompatible
is that
incommensurable is (mathematics) of two real numbers, such that their ratio is not a fraction of two integers while
incompatible is of two things: that cannot coexist; not congruous because of differences; irreconcilable; disagreeing.
As nouns the difference between incommensurable and incompatible
is that
incommensurable is an incommensurable value or quantity; an irrational number while
incompatible is (medicine|chemistry|chiefly|in the plural) an incompatible substance; one of a group of things that cannot be placed or used together because of a change of chemical composition or opposing medicinal qualities.