I recently sailed on the Caribbean Princess and had an AA category mini-suite on the Dolphin deck (D525), midship. I was actually upgraded from an AD category mini-suite from one deck lower.
The majority of the outside staterooms on the Dolphin deck are mini-suites with balconies, but the drawback of the balconies on this deck is that they are not covered. If the weather is rainy, forget about sitting on the balcony. Balconies on higher decks are partially or fully covered.
Also, there is little privacy on the Dolphin deck balconies, as the ship is designed in such a way that passengers with balcony staterooms on higher decks can look down and see you.
Another caution about the Dolphin deck: it is directly above the deck where the tender boats (lifeboats) are attached. I was rudely awakened very early in the morning of the day the ship anchored off Princess Cays, by the sound of the tender boat winch lowering the boats.
Given these minor drawbacks, however, the mini-suite category was great as it had a bathtub instead of a shower. (One of the ship comedians was making jokes about the small showers and I had no idea what he was talking about!)