This really depends on what you are looking for. The BD is alittle more refined, slightly "up scale" dining. Quiet and relaxed. The 50's PT is anything but quiet and relaxed.
The servers at PT interact with the guests, acting like your mother, little sister, big brother, crazy uncle, etc. depending on the servers age and gender. The setting is as if you were eating in Mom's kitchen and the cooking in good old down home fare. You will be repremanded if you forget your manners (no elbows on the table, washing your hands before you eat, etc.) The interaction really depends on the guest reactions. If they see you don't want bothered they ease up.
I once accidently broke a water glass and was made to stand in the corner while the entire room said "shame, shame on you!" It was a little embarassing, but all in good fun!! Our family LOVES the 50's PT. We love the servers being silly and the food is pretty good too. (You gotta try the S'mores for dessert!) The food at the BD is also very very good, but the atmosphere seemed a little stuffy to us.
Which ever you choose I am sure you will have a great meal. Why not try them both??