Both weapons work with the default special ability and have their own specific characteristics. That is, with an axe in the right hand and a sword in the left, both will receive bonuses from the one-handed weapon skill ranks, plus the sword will receive bonuses from the sword skill tree, and the axe will receive bonuses from the axe skill tree.
But does the bonus to hit chance from swords stack up to a total of x3 when parrying?