I'd go with Kyoto. Osaka is much like Tokyo - big, modern, high-energy, albeit with its own vibe. You will have already had several days in ultra modern Japan. Kyoto will give you a much different experience than the "big cities."

Many disagree with me but I have never really found any good reason to stay in Osaka other than a transit layover near the shinkansen station. Visit, yes. See some sights and have a great meal, yes. But for the stay, I much prefer Kyoto - or even Nara. Despite no club floor, the Kyoto HR is quite nice and in a really great location. Assuming you invest in a JR Rail Pass, the bullet train between Kyoto and Osaka takes only minutes so a day visit is no sweat.