So, what's the consensus on the best weapon, speaking purely on how much damage it can put out before depleting a stamina bar?
In addition to Fireworker's post, I'll add that damage per stamina is generally less important than damage per second (damage per swing divided by swing speed).
This is because situations where you actually have an opportunity to dump an entire stamina bar into a single enemy are relatively rare. It's much more common to have a limited opening to get some hits off before you have to dodge. In those situations it's more important that you do as much damage as possible during that limited window, since you'll regenerate your stamina quickly as soon as you're not swinging.
Now, there are situations where damage per stamina is most important: specifically, when you're stunlocking humanoid enemies with a quick weapon. In these cases your ability to stunlock lasts as long as your stamina bar, and so damage per stamina is the governing consideration.
And there are also situations where damage per second is less important than damage per swing - particularly aggressive bosses, for instance, who will only ever give you the opportunity to get off one or two attacks at a time. Similarly, certain large enemies can only be reliably staggered by hits from slow, heavy weapons, and a weapon that can stunlock an enemy is always going to be a better choice even if it's doing less damage per second.
Finally, some weapons are better at some levels of stat investment than others. A specialized weapon like the Reiterpallasch looks much better compared to other weapons at 40 points of stat investment than it does at at 80 points of stat investment, and a quality weapon like Ludwig's looks much better at 80 points of stat investment than it does at 40.
Having said all that, there is actually an answer to your question. The weapon that does the most damage per second at most common levels of stat investment is the blood-form Chikage in a bloodtinge build. This weapon is balanced by the fact that it slowly drains your health, doesn't have much of a moveset, and scales with different stats in its two forms.
Beyond the Chikage it's pretty tough to single out any particular weapon as "doing more damage" than any others, though. They all have their situational uses.
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