You didn't specify any kind of context within which the performance should be compared. In most cases the fact that enum
members are objects is completely irrelevant because only the reference values are being compared; the objects themselves are not even touched.
However, public static final int
are compile-time constants, and their values are hardcoded at the place of usage, which clearly imposes no overhead at all.
So it's very little overhead against no overhead at all, but at the expense of problems with compile-time constants, such that changing any of them requires recompiling everything which references it.