What is the difference between the written play and the film version of Pygmalion?

The major difference between the play Pygmalion and the musical film (dubbed My Fair Lady) that it was later made into is also one of the most controversial aspects of its adaptation. This difference is quite simply the ending of the story. 

Pygmalion finishes with great emotional distance between its two protagonists. After continued conflict between Higgins and Eliza, Eliza proclaims that she is prepared to marry Freddy, her timid suitor, and leave Higgin's household permanently. Eliza and Mrs. Higgins leave to attend Eliza's father's wedding, but not before Higgins demands that she complete a series of ridiculous errands (pick up ham and Stilton cheese and purchase reindeer gloves and a new tie). Eliza boldly orders Higgins to, "Buy them yourself." She sweeps out defiantly, leaving Higgins in a cloud of deep denial. The play's ending is absolutely clear: the two will part ways. Eliza is a student who has outgrown her teacher; she now possesses the skills and confidence to independently make something of herself in the world. Higgins will have to continue on in his delusions of self-importance without her.

My Fair Lady, on the other hand, treats the ending of the play with what some  critics believe to be a disgraceful dose of sentimentality. Rather than Eliza returning to Higgins to tell him off one last time, the movie shows Higgins going off in search of Eliza after her disappearance. He manages to find her at his mother's house. Eliza delivers to Higgins the same information: she will be marrying Freddy and does not plan to see him again. Higgins returns home and breaks into a melancholic refrain of the song "I've Become Accustomed to Her Face." He listens to recordings of Eliza's voice on his phonograph, pining for her company. Eliza reappears in his study and shuts off the record, proclaiming coyly in her original accent, "I washed my hands and face before I come, I did." Astonished, Higgins whispers, "Eliza... where the devil are my slippers?" The exchange seems to sweetly recognize the pair's origins: Eliza's openness and vulnerability and Higgin's willing spirit. As the music swells, Eliza approaches Higgins, smiling at him tenderly. This ending, although not concrete, implies that Eliza and Higgins will end up a couple and that Eliza will not marry silly, ineffectual Freddy after all. Many find this deeply problematic in that it erases the positive and independent qualities that Eliza was supposed to have gained over the course of the story.