I also appreciate that Eliza is given a great deal more credit in the play. I understand why the musical would choice to make Eliza struggle to learn to even hear the phonemic differences in her pronunciation; it after all provided a great opportunity for another musical inset. However, it really strengthens the legitimacy of her ire with Higgins after the garden party (as it is in the play) that she was from the very beginning a gifted student of phonetics. It equalizes to a greater extent the roles of learner and teacher and makes their achievement much more a partnered win. It makes his taking all the credit that much more grievous.
Lastly, by comparison, I love that at Prof. Higgins last request of Eliza in the play is met with "buy them yourself" whereas in the film his last request of her are the last words spoken and we don't get to be privy to her response. I am glad she has a chance to show her backbone a bit more.