Jar, an automaton WILL outnuke a BLM on a case-by-case basis, and often over time as well. Even in Abyssea.
But they are restricted by cast timers and maneuvers, BLMs are not. BLMs are limited by enmity however. If a BLM can ride the enmity train without crippling it's casting, it can indeed get ahead of a PUP. But very few BLMs have those skills. Mana Wall and Enmity Douse are crutches designed to close the gap with PUP, not steam ahead.