I’m no expert, these are my opinions only
My weapons progressions is almost always:
knife spear -> steel spear -> quiang -> broadsword or katana.
For general use: Katana
The rapid strike procs more then enough to make up for slightly lesser damage especially when you get good skill and are critting + rapid striking often.
Nobody calculates that in when they determine dps for weapons.
Also it’s one of the best weapons for the best melee martial art, Niten Ichi-ryū.
For me personally, the broadsword.
I run high strength PCs with heavy ~35+ torso/arm/leg encumbrance. I don’t do a lot of dodging so the extra +1, and the block are much needed. I’m super durable, so I don’t mind if the fight takes a couple extra turns. Now If I find a Niten Ichi-ryū book, it’s all Katana all the time.
The battle axe looks good on paper, but it doesn’t have block, parry, or quick strike.
Like you said, damage isn’t everything. I guess if you ran a lightly armored PC you could make a battle axe work. But you would get shot to pieces the first time somebody decides to shoot you.
EDIT:
I always keep a knife spear, steel spear, or qiang in the backpack for armored enemies or enemies that spray acid when hit.