Oh, one of these is definitely going to laughably overpower the other. I’m just not sure which one it’d be. The staff has reach, the rapier has speed and has the advantage of stabby stabby over blunt force trauma. It’s really going to be a question of whether or not both fighters know how to use their weapon’s advantages to the fullest extent. What’s going to keep it a “fair” in the understanding that any non-same weapons used in a fight is never fair, then it’s going to come down a question of skill.
The staff wielder is going to have the advantage so long as she can keep the other woman with the rapier at a distance. The woman with the rapier will have the advantage if she can find a way to maneuver herself into striking range without taking too much debilitating damage from staff strikes. The rapier has to be aggressive in this situation, while the staff wielder is fighting a battle of attrition. All they need to do is wear their opponent down and keep giving them knocks until they can’t lift the sword anymore. They can also attack the legs and feet more readily and safely than the one with the rapier.
All I can say is whoever takes the initiative here is going to keep it and that’s not at all helpful, I know.
I’d look at Scholagladitoria’s Quarterstaff vs Sword, pt 2, pt 3.
Then, look at this video from EnglishMartialArts in response to those videos about the merits of the quarterstaff.
Now, these are about quaterstaffs versus sword because the quarterstaff is the standard European staff and the bo-staff is a Japanese staff.
When I’m responding in these videos, I’m basically assuming that these two women are training in the same style. It should go without saying that bojutsu and other styles are meant for combat against weapons from their same region. On some level, there’s going to be a lot of similarities with staff techniques (though looking at the wide variety of usages and developments of the weapon worldwide, that’s not necessarily true) but what a weapon style was designed to deal with will obviously massively effect the techniques used. There is no comparative sword to the rapier in Japanese martial arts. Whereas techniques with the European quarterstaff involve the skills and strategies for facing a wide variety of swords because there was a greater likelihood of facing one. So, the movement patterns one might use to fend off a katana won’t completely translate
(at all) when faced with a rapier.
So, I’m just throwing that out there.
One of the trickiest aspects of writing with weapons is realizing that most of them, even if there is a similar version present in another culture, are limited by what their practitioners expected to face. If you’re using from a weapon that comes from a culture with a lot of cross-pollination and a lot of variance because it’s people were constantly dealing with different cultures or a lot of massively different styles of combat then it’s going to have an inherent advantage over a weapon and style that comes from a culture that doesn’t have that. (That weapon will probaby still have an advantage in it’s home environment though.) There’s more expectation of the unexpected, more variance, more likelihood you may be facing a kind of opposition or new tactic that you’ve never seen before.
I am, however, assuming that these two are from the same school and trained in the same style, they are just using different weapons.