The Chu Ko Nu/Zhung Nu doesn't sound like something you'd want to use against heavily armored infantry, with Ming dynasty texts apparently recommending that the bolts are poisoned to make up for the lack of penetrating power. It's also apparently rather inaccurate and short ranged, with an effective range of 60-80 yards. It seems that its main use was as a siege weapon, mounted on walls, enabling the defenders to pepper the enemy during an assault.
I'm curious as to what Chinese/Roman battle you're referring to. There's unsubstantiated belief that a small number of Romans may have escaped the Parthians after being captured at Carrhae in 53BC, finding shelter among the Huns who were then stomped on by the Chinese near Tashkent in 36BC. Even if the account is true, the battle is hardly an endorsement of the superiority of the Chinese military over that of the Romans. Any Romans at the battle would have been a relatively minor contingent, and more importantly would have been somewhat past their prime, after anything up to 17 years of captivity.
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