It's certainly not a clear divide, but 日付 is a more formal word that tends to be used in abstract settings such as 「日付・時刻」 on device setting menus, or 日付順 ("in datewise chronological order"), whereas 日にち is used exclusively for the date of a specific event (大会の日にち, the date of the conference; 〜の日にちを選ぶ, to choose a date for ~).