You already have a very thorough discussion of these two characters in Pygmalion. I would simply add a couple of things. Pickeringis, indeed, a rather harmless foil to Higgins, and he is the one who treats Liza with respect and dignity. She is quite clear as she talks to the Colonel in Act V--she is appreciative of his help and recognizes he would have done the same with anyone because that's just who he is. On the other side of that, though, he certainly could have limited Higgins's bullying and nagging. Instead, he benignly watches the process and doesn't intervene much at all. It's true that Liza was not in mortal danger, of course, but he certainly could have been more involved and shown more compassion. It works out, though, and Liza is grateful. She says to him:
You see, really and truly, apart from the things anyone can pick up (the dressing and the proper way of speaking, and so on), the difference between a lady and a flower girl is not how she behaves, but how she's treated. I shall always be a flower girl to Professor Higgins, because he always treats me as a flower girl, and always will; but I know I can be a lady to you, because you always treat me as a lady, and always will.
Higgins is a bully, but he got the job done. He does so rather heartlessly, treating Liza as an experiment rather than a fellow human being. In fact, when she points that out to him, Higgins proudly proclaims that he treats everyone that way--king or peasant is all the same to him. This is his flaw, of course; people don't really matter except how they fit into his plans. (Just ask his mother--she would agree.)
Perhaps it is true that these two men are two sides of a coin or two parts of a whole. If so, they can both take credit for the accomplishment of turning Liza into a "lady." But only one of them does, of course, and that's Higgins.