The only difference is in the base attack.

AP halves the armor protection, but not all axes and maces are created equal.

For example, the mace of a Teutonic Knight has a base attack of 13. The mace of a Mamluk Archer has a base attack of 8. Clearly, the Teutonic Knight's mace is a lot better at killing things — armored or unarmored — than a Mamluke Archer's.