Umm~ BLM can out nuke BLM?
In either case its time which kills SCH. BLM has no JAs it must rely on for speed or power, SCH needs Alacrity or Ebullience to put it above BLM because BLM has the ability to cap Cast Time Reduction where as SCH can not, in the best possible SCH Fast Cast set you get around 60% now I think, where as BLM has a native 50% and can use gear to easily cap. Once strats run out SCH loses some speed, BLM ends up casting almost twice as fast which puts its DPS a lot higher. This comes back on BLM though when they run out of MP, so without a stable way to keep their MP up they eventually lose out again.
BLM's real advantage over SCH is sadly AoE spells, kinda like how WHM has their Curaga spells over SCH, but WHM has more than just that going for them while BLM really doesn't.