Depends on a couple of things. Backstage does not guarantee the whale, but Dining does. Also, Dining is later in the day--more like an early dinner. Backstage is around lunch time. We went in June and Backstage was at noon and 2:15 pm. I think Dining was around 4:30 pm. We did Backstage because we wanted to leave Seaworld by 5 pm. It was well worth the money, no matter which one you choose.
Since I have never done Dining, I don't know if they do anything else "special" besides guarantee the whale.