Up until the early 70s Tony lead vs featured/supporting was done by billing. Bosley, Grimes and Bancroft were all billed below the title or in less-than-star billing.
Barbra and Sydney Chaplin were both star billed above the title.
In 1964 no one was tired of Barbra. She was the New Girl In Town with her face on major magazines like Time, Life and Look. Carol won because she gave a terrific comedic performance in a production that was worthy of her work.
Funny Girl has a terrific score, one of the best, but Dolly's production used its score better. Also Dolly had something else that Funny Girl didn't have--Gower Champion.
This was a really great season. No one has even mentioned High Spirits (flawed but fun and with the great Bea Lillie), Foxy (a failure but fun with the great Bert Lahr), The Girl Who Came to Supper (Noel Coward's last), the mediocre Here's Love, Mary Martin in her only bona fide failure, Jennie (with a good Dietz/Schwartz score), or What Makes Sammy Run? (good score, great star performance, otherwise so-so). And then there is Anyone Can Whistle, but so much has been written about that.
And the plays were good too: Luther, Chips With Everything, Dylan, The Rehearsal, After The Fall, Spoon River, Barefoot in the Park, Hamlet, Any Wednesday, etc, etc.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher