In a large scale war I'm favoring Kansaro. He is SBS's rhm and thus should be more familiar with such responsibility
Managing large armies is not something anyone can do. Gyou'Un for example would probably trash any Heavenly King in a small scale war, but if the numbers are there then he's losing to experienced leaders like Kyou'En or Genpo
Kansaro still has no real feats other than that surprise attack but that's the level of portrayal I think he deserves, for now at least.
Small scale wars are where Rinko would shine
As for the duel, it is nothing short of an extreme diff either way. I went over Rinko's combat ability before, here's a short summary
Reasons why Rinko lost in Sanyou
-Underestimating Shin -as told by Rinko- had him lose his fingers on the first day
-Shin growing stronger the more competent his opponent is (and borrowing some of that strong ass Ouki weight)
-Even with one hand Rinko would've won if not for outside interferance
Man was toying with both Ouhon and Shin at one point
For now I'm leaning Rinko, I don't think Kansaro is that strong of a warrior, but it can change based on new info