All three DR's are very similar. Same service level, same menu, etc. If you have looked at the deck plans on Princess.com, you will know that they are located at Mid-Ship Deck 6, Aft Deck 6, and Mid-Ship Deck 5. One difference is that a section of the Deck 6 Mid-Ship is set aside for Club Class dining. You will find table sizes from 2-top to 10-top in all DR's.
If you are eating on variable times each day, you can ask at the door for private or sharing. You may have to wait longer for a private table, depending on timing and demand when you show up. You can book a table ahead of time using the MC App (DineMyWay feature). You can also do this using the cabin TV.
No DR is better than the other with the exception of location. Some like the aft DR is their cabin is towards end of ship. Those with cabins more forward most likely prefer the mid-ship DR's due to proximity.