There are actually very few extant jo schools. It really wasn't a very significant weapon in the Edo period. Furthermore, there was a symbolic valence in the use of the sword in uchi-tachi, as that was the core symbolic weapon of the bushi.
That said, here is an example of sword vs bo
Araki-ryu has sword against bo and against naginata kata, where the sword wins.
I'm sure there are a lot more, even among the appr 100 surviving ryuha in Japan. But there's a couple of examples.
Could anyone point me to some kata of ken vs jo or ken vs naginata where the kenshi wins? Every ken tai ko or ken tai naginata kata I see, the jo ends up winning.
Now of course, a naginata is straight up more dangerous than a katana like a rifle vs a handgun so no question there. But a jo is a different proposition. It is only slightly longer than a katana though with the ability to extend / retract thanks to hand movement, so it's better at controlling distance.
However, the jo can be grabbed, the katana can't. And there's a long time during Edo period where various koryu schools develop techniques to use against jo. I find it strange that there's no anti-jo kata to be found for a kenshi.