Oathbreaker's End is a battle axe, but it is also a two-handed weapon (unlike standard battle axes). It currently do not benefit from the wielder wearing "Helm of the Falcon".
Specifically the effect associated with the helm, "Raptor`s Grip" (-10% recovery time for 2-handed weapons). On other 2-handers the effect show in the tooltip when the mouse hover over.
Hope this helps to solve it IF it is not intended.