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.
Professor Henry Higgins - Henry Higgins is a professor of phonetics who plays Pygmalion to Eliza Doolittle's Galatea. He is the author of Higgins' Universal Alphabet, believes in concepts like visible speech, and uses all manner of recording and photographic material to document his phonetic subjects, reducing people and their dialects into what he sees as readily understandable units. He is an unconventional man, who goes in the opposite direction from the rest of society in most matters. Indeed, he is impatient with high society, forgetful in his public graces, and poorly considerate of normal social niceties--the only reason the world has not turned against him is because he is at heart a good and harmless man. His biggest fault is that he can be a bully.
Colonel Pickering - Colonel Pickering, the author of Spoken Sanskrit, is a match for Higgins (although somewhat less obsessive) in his passion for phonetics. But where Higgins is a boorish, careless bully, Pickering is always considerate and a genuinely gentleman. He says little of note in the play, and appears most of all to be a civilized foil to Higgins' barefoot, absentminded crazy professor. He helps in the Eliza Doolittle experiment by making a wager of it, saying he will cover the costs of the experiment if Higgins does indeed make a convincing duchess of her. However, while Higgins only manages to teach Eliza pronunciations, it is Pickering's thoughtful treatment towards Eliza that teaches her to respect herself.