Battle Sword is essentially a Gladius.
Better to just skip it and use a Bastard Sword (it looks nicer too).
Except glads are ugly.
And having done the math.. when paired with the battle sword..... the two egos are ridiculously even, battle/bastard. (and by association glad since it's about the same as battle)
Bastard/full max damage battle is 15 max damage ahead of battle/glad ego with a matching battle, and the latter combo is 15 crit ahead of the battle combo. So it's simply a choice of 15 max or 15 crit. Basically, do you smash or do you wm lol.
Using a cutlass gives you about 3 more max and 5 more crit than the battle combo. Small enough of a difference imo to be worth sacrificing for looks/ease of repair if you felt so inclined.
As for mura compared to cutlass, it's 7 more max and 5 less crit. So mura is still the best balance.
This is all taking into account the way crit is averaged for dual wield, but damage stacks for wm/smash. This all doesn't hold true if for some reason you were single wielding any of these lol. (ie; elf melee... but who does that other than me really >.>)