Dive Oahu is a great group, provides pickups from Waikiki hotels, and dives out of Kewalo Basin (right near Waikiki). They tend to dive deep (100 feet, or so) the first dive on one of the three ship wrecks in the area, and then move shallow for the second dive where the corals are in 20-40 feet of water.
Island Divers Hawaii typically stays in the Maunalua Basin area and will typically dive the Corsair or one of the sunk barges, followed by a shallow dive in the area. On occasion they can dive China Wall (Koko Head) if the water conditions are good, and the customers on board are comfortable with that kind of dive.
As a personal preference, I think the corals are nicer and more abundant in the Waikiki area, and I also like the wrecks that are available there better, too. If you have the time, you can give both groups a bit of business and dive multiple locations.