Eliza and Higgins are characters who share a few things in common, and then drastically turn incompatible when specific events take place and shake the foundation of the scam that originally brings them together.
In both, Eliza and Higgins, we encounter two very passionate individuals who are quite safe within their own skin. They know who they are, and they are quite content with it. None of them believes that neither should be asked to change a thing about their personalities. In fact, the only reason why Eliza comes to get the phonetic lessons from Higgins is not because she isn't happy with herself, but because she looks forward to better work opportunities.
Eliza and Higgins are also stubborn, and assertive. They, unfortunately, also suffer from pugnacity when it comes to their anger. We see this in Acts 1, 4 and 5, particularly, where the dialogues in which Eliza and Higgins are involved are quite spiced, strong, and somewhat vituperous.
In contrast, Eliza is certainly a kinder and much humane than Higgins. She does show a certain quality of submissiveness when she pulls Higgins slippers, for example, and when she quietly listens to his rants. Eliza's feelings also get hurt several time in the play, which tells us that she is nevertheless a sentimental person who needs to feel appreciated. Eliza is no stranger to hard work, nor to a classicist society who view her as a lesser person. However, even with these elements have helped her develop a core of tolerance, she is still a tender person inside. Eliza is what we could compare to a modern day social survivor.
Higgins is an eternal bachelor. He is selfish in action, thought, and word. He is stubborn and inept for change. He is rash, bawdy, is oblivious to social decorum, and even to marginally adequate mannerisms. He seems so obsessed with his work that he has lost touched with his humanity, or that of others. He is hurtful, calculating, cold, and matter-of-fact. He is the anti-hero of melodrama; the epitome of the anti-romantic man. So much he is, that in the end he continues life as usual. This shows us the type of brash person he is that can only live for one instance of something that may or may not make a difference in his life.
In all Eliza and Higgins's similarities are what make their differences so powerfully charged when they argue and disagree. This is what makes for great drama in a play, and perhaps a great technique employed by Shaw to demonstrate the uniqueness of his characters.