There are Pros and Cons to Belize city VS Ambergis Cay;
Belize City is dismal, and third world once you step outside the hotel, HOWEVER you have the oportunity to go water tubing in caves, jungle tours, Myan ruins, etc... outside of Belize city if you want some land excursions.
Ambergis Cay has more day trip oportunities, if you want to spend your time diving, and you have to use the locals for diving that area since they've cut all the mooring lines and hacksawed the pins once used by Nekton, and the other two liveaboards. Ambergis is limited in shore type excursions though, so my best advice is to decide if you'd rather have more dives, or shore excursions for those three days. You'll be able to dive 25-30 dives on Nekton |Pilot while you're aboard.
Good luck with your decision, and have fun with the crew on the Nekton Pilot... they are a riot|!