The answer's in the question. Photoshop is best suited to photographic manipulation, while Painter is best suited to digital painting and illustration. The only real similarity is that they offer some form of image manipulation, but their focus is quite different. So there isn't really a case for one or the other, it depends on what you need to do.
Having said that, Photoshop is much more of an all-round tool than Painter, allowing you to create 2D graphics for things like the web and print among other features. Painter aims to recreate natural media effects - brushes, paints, textures and so on.