I stayed at the St Regis Osaka a few years ago. It was the most enjoyable hotel stay I've ever had. It's right near the big food district in Osaka, which is world class, and very close to the entrance to the shopping arcade, which leads to the legendary Dotonburi. Osaka is my favorite city in Japan - I love the food - it's the same legendary quality as in Tokyo, but cheaper - and the vibe is totally different from Tokyo.
I found the hotels in Kyoto (including the Ritz) to be a bit of a letdown. Kyoto itself is marvelous, but the hotels are generally subpar, even by Japanese standards.
I would choose the StR Osaka.