Both 華誕 and 誕辰 are more respectful ways of saying 生日 (birthday).
For 華誕, I have seen: "最高元首華誕", "蘇丹華誕", "日本皇華誕".
For 誕辰, I have seen: "國父誕辰", "先知默罕默德誕辰".
Sometimes, within a text, I see 華誕 being consistently used for the birthday of a particular person, and 誕辰 being used exclusively for the birthday of another person. So I wonder: is there a convention for selecting one over the other for particular "types" of people, or is selection completely arbitrary and always interchangeable?