I have never stayed in or dove from Cancun, so I can't give you any meaningful comparison. However, IMHO, the diving on Cozumel compares favorably to just about anywhere in the Caribbean. I've been going to Cozumel for over 20 years now, and I keep going back because I love the diving. And no, Cozumel is most definitely NOT more expensive than Cancun -- its the other way around. You can find quite acceptable lodging in Cozumel for as little as $35 US a night -- not on the beach or waterfront, but still nice. As to waterfront resorts, hotels, there are several choices that fit your needs, including Scuba Club Cozumel, Hotel Cozumel, Blue Angel, Casa Del Mar, and any of several Resorts to the south. All have very close access to the water, and shore diving. Of these, I have only stayed at Hotel Cozumel (very nice resort and close to town, but I would NOT do the AI Plan, as the food simply stinks) and Casa Del Mar (smaller and more intimate than Hotel Cozumel, farther south and closer to dive sites but a taxi ride into town where most of the restaurants are, breakfast included with room). My personal preference is NOT to go AI, because I really enjoy good food, and Cozumel has a wealth of good restaurants, most of which are downtown. You can eat well even at the cheaper locally owned spots - the Loncherias (not open for dinner) that serve the Comida Corrida, a fixed price full lunch, are some of the best bargains. Or you can splurge, and for $40-$50 per person, you can have a great dinner at places like Kinte, Kondessa, La Cocay, or others. But if you are not into food, then maybe an AI would fit. Best thing I can say about the AI at Hotel Cozumel is that alcohol is included, so if you like to drink a lot on vacation, you can get your money's worth at the bar and still eat the occasional lunch or dinner out if you can't stand the tasteless buffet it serves up.
Which dive op to use is a whole new discussion. You do NOT need to use the house dive op at any of the resorts - all will allow other Dive Ops to pick up at their pier (though some will charge a pier fee). The house dive op at Hotel Cozumel is Dive Paradise, and while they are a perfectly acceptable operator, and I have been diving with them, they would not be my own first choice - I like a valet operator like Aldora, which uses HP Steel tanks (I get a Steel 120, lots of air, better buoyancy characteristics than Aluminum), dives small fast boats, spends a long SI on the beach for better outgassing & longer second dive. Which Dive Op is right for you depends on your own likes and preferences, so please don't ask "which is the best Dive Op" without giving specifics as to what you are looking for.