I prefer Elizabeth. I love how varied the diminutives are, so you can find one that really suits the girl's personality: Liz, Lizzie, Liza, Eliza, Beth, Betty, Libby etc. It's a wonderful name.
I like Cordelia but associate it too heavily with King Lear - such a bitter, sad story, even though she is the heroine. And I'm not wild about the "Cor' sound.