For the sake of argument, can someone argue why Coz is better than Grand Cayman? I need convincing...
"Better than" is such a subjective judgment -- I would never try to tell someone else that one vacation destination was "better than" another, since we all have different tastes, priorities, desires. However, I can tell you why I prefer Cozumel; I'll let you make up your own mind about what is better for you. Disclaimer - while I've been to Cozumel 4 times in the last two years, and going back in December, it has been more than 5 years since I was in Grand Cayman, so my info may be dated.
1. DIVING -- the diving is great in Grand Cayman, but fixed mooring diving is harder work for me. I'm old, fat and not in the best shape of my life. I really enjoy the drift diving, where the hardest work I have to do is climb back on the boat at the end of the dive (or maneuver through ironstone at the end of a shore dive). And diving is a much better value in Cozumel. In Grand Cayman, I found it hard to find a dive operator that charged less than $100 for a 2-tank dive, and that pricing was in Cayman Dollars, which means it was really $125. Without tip. I have been diving with Aldora, one of the highest priced Ops on Cozumel (but well worth it, for the HP Steel 120 tanks, the long SI at a beach club, the great valet service, and the great DMs, IMO), and I think I only paid $85 US plus tip at the time (it was a few years ago) for two dives where I had more than an hour of bottom time on each dive. You can also find many dive ops in Cozumel where, on a multi-day package, your cost for 2-tank boat dives is $60 US or less, a price that no one on Grand Cayman comes even close to. And, frankly, IMO, Cozumel has walls, reef structure, and sea life that can match or exceed anything Grand Cayman has to offer.
2. DINING -- Frankly, some of my very favorite restaurants are in Cozumel, and I can get a great fine dining meal without breaking the bank. And I can also get very good, tasty and filling local dishes at any of a great many locally owned restaurants and loncherias for dirt cheap. Every trip I make to Cozumel I would go back to Sabores, a little loncheria south of the square, and have a great 3-course lunch for 70 Pesos, plus tip. That's a total, with tip, of about $7. There are just no "cheap eats" on Grand Cayman, at least as far as I was able to find. Food on Grand Cayman is just plain expensive. I had a fish sandwich at one place on the waterfront there, I forget the name, and it was $12 in Cayman Dollars (meaning it was really $15 US) before tip and without a drink. And, while fine dining is certainly available in Grand Cayman, a really good dinner there will set you back $100 US or more per person. I've had really excellent meals in Cozumel for less than $40 US, and that included appetizer, desert and a cocktail. For quality, variety, and value in dining, I think Cozumel is miles ahead of Grand Cayman.
3. LODGING -- when last I stayed in Grand Cayman, I opted for the "cheap" lodging, a small B&B that, with tax, cost me nearly $100 US per night. The big Resorts on Grand Cayman will charge $180 US or more per night. I don't typically stay at the most high-end places on Cozumel, places like Cozumel Palace, or the Grand Occidental. But I can get very nice lodging at places like Casa Mexicana downtown (a nice hotel, not a resort) for about $65 US a night, or Casa Del Mar (more of a resort, with pool and smallish beach area) for about $90 US a night, and both prices include all taxes and breakfast in the morning. If I want to go "cheap" in Cozumel, I can find very adequate rooms for $35 US a night or even less, and get quality and service equal to or better than my $100 US a night B&B in Grand Cayman. IMO, Cozumel is a much better value for lodging than Grand Cayman.
4. ATMOSPHERE -- I would never call the people of Grand Cayman unfriendly, but there is not nearly the feeling of warmth and welcome that I get most places in Cozumel. Grand Cayman seems to take tourists for granted, you are always treated politely and cordially, but you are certainly not treated as part of the family or community, the way you will be in many places on Cozumel. When you keep coming back, you see the same people, the same DMs, the same Hotel bell hops, the same waiters, waitresses, and restaurant owners, and they remember your name and treat you as a friend. Now maybe that would happen in Grand Cayman, too, if I came back year after year. I just can't afford that many trips to Grand Cayman, so I'll never find out.