On page 9 of Kauffman's Formal Knot theory, Kauffman claims

The Alexander-Conway Polynomial is a true refinement of the Alexander Polynomial. Because it is defined absolutely (rather than up to sign and powers of variables) it is capable of distinguishing many links from their mirror images - a capability not available to the Alexander polynomial

Does anybody know of any examples of this happening? Or when two knots have the same Alexander polynomial but different Alexander-Conway polynomials?