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Battle takes place on neutral ground

Well, if we bar Barriss' showing against Anakin and brand it as PIS, then frankly, Atris wins.

Eh, Barriss us arguably the better force user due to her more impressive TK.

Atris wins.

Her TK is irrelevant though, because this is sabers only.

All we know about Atris really is that she's a master of lightsaber combat, and primarily a Juyo practitioner. Also that she's not as good as Meetra is.

Is that enough to give her an advantage against Barriss? Well, possibly...