Even at DA+10 (the reward before mirrors) it will add more damage over time when factoring the shorter tp phase from increased DAs and the increased damage from additional DA procs on WS.
It obviously depends on the server but a Fire Axe costs around 3mil when lucky price shopping on Bismarck and a DA axe finished runs 2-3mil when price shopping so the cost is on par.
I don't recall ever mathing out a situation where the OAX Axes actually beat a STR path let alone a DA axe, lower base damage combined with the bad multi hit distribution really hurt these axes.