In my opinion, both Adler and Holmes end up winning in this case.
You can argue that Adler has won because she really outsmarts Holmes. At the end of the story, Holmes has still not managed to get the picture away from her. She figured his plan out and managed to make sure he couldn't get the picture.
You can argue that Holmes wins because he gets what his client wants. His client is happy with the way things turned out so that seems like a good thing for him.
But I imagine Holmes would say that he lost because he got outsmarted and his client only got what he wanted because Adler let him off the hook.