In August 2009 we stayed for 2 weeks at the Cozumel Palace, and decided to dive with Aqua Safari, rather than Aqua World.
The Cozumel Palace was previously called Plaza Las Glorias, but the hotel got bought by the Palace Hotel chain and completely renovated and upgraded. It's an all-inclusive hotel.
Before booking this hotel we read many reviews of various all-inclusive hotels on Cozumel. For most of them we found that travelers reported quite some negatives, such as limitations on how often you can eat in the on-site restaurants, noise, or the constant nuisance of agents trying to sell you time shares. NONE of that at the Cozumel Palace. NO limitations. You can eat at each of their restaurants as often as you want, and there is even unlimited room-service (food/drinks) 24hrs a day, and even the mini-bar and the liquor on the room is free. Every room has a perfect ocean view. We were reeeally happy with the hotel. Normally it would be beyond our budget, but there were very good deals available when we booked (Orbitz).
The on-site dive operator at Plaza Las Glorias/Cozumel Palace used to be Aqua Safari (http://www.aquasafari.com/). The Cozumel Palace hotel has recently replaced Aqua Safari with Aqua World (http://www.aquaworld.com.mx/), which is a chain that provides all water sport activities at all Palace Hotels in the Carribbean. Aqua World has a retail shop at the Cozumel Palace hotel now, and they do rent tanks for the occasional shore dive ($7), but it's not the same full-fledged dive center that it was when Aqua Safari was in the hotel. Aqua World's main location on Cozumel is further down the coast.
We decided to dive with Aqua Safari, which was a good choice. Their boat picked us up at the hotel pier, their service was great, and their downtown dive center is only a short walk away. At the Cozumel Palace we had lockers where we could store the gear, even the rental gear that we got from Aqua Safari. Aqua Safari was very accommodating with everything.
Surprisingly, the rinse tanks at the Cozumel Palace hotel did not have plugs, so you could not fill them with water. We asked Aqua World several times, but in a 2-week period they were not able to get the rinse tanks working. So all divers used the nearby showers to rinse their gear. Also, all hotel rooms in the Cozumel Palace have a jacuzzi which can also serve as de-luxe rinse tanks... :-)
The diving was great. We were lucky and saw turtles almost every day. A few times we saw nurse sharks, very large green eels, and a couple of toad fish.