We know that the other states go out of their way to avoid full blow conflicts with Chu, although we know that fights did happen, like Kanmei vs Oukotsu and Kanmei having fought battles against all other states except Yan. But that being said, I still don't think there would have been many occasions for a Kouen/Renpa clash and thus neither do I think they were "consistent rivals".
In contrast, Renpa in particular kept on mentioning the Qin Six. Zhao's Great Heavens consistently fought against them. Renpa talked about the "golden era" created by the GHs and the Qin Six, those Qin "bastards" were the ones to keep his flame completely alive and he grieved their departure from the world. Heck, he talked about them even to Gaku Jou shortly after deafting him. They clearly were his rivals.
That being said, Renpa obviously knows who Kouen is and has huge acknowledment for him at least (as we saw when he was talking with the Chu king). Kouen is probably someone like Gakuki was (I think) - that would be an enormously powerful commander who wasn't a consistent rival to the Qin Six/3GHs.