The code here is somewhat contrived in favour of the ints. Taking the meat of the | example…

    int a = A | B | G;
    for (int i = 0; i < 1_000_000_000; i++) {
        int b = A | B | G;
        assert a == b;
    }

This is actually compiled as

    int a = 67;
    for (int i = 0; i < 1_000_000_000; i++) {
        int b = 67;
        assert a == b;
    }

The compiler should trivially identify that a == b is always true.

This simple change to the Enum case brings it to within 3x the int scenario…

    Set<Flag> a = EnumSet.of(Flag.A, Flag.B, Flag.G);
    Set<Flag> b = EnumSet.of(Flag.A, Flag.B, Flag.G);
    for (int i = 0; i < 1_000_000_000; i++) {
        assert a.equals(b);
    }

A better range of benchmark cases is required.