Thanks to you all! Let's suppose I do both, what's the most optimal way to arrange the visit? Here are the parameters. I'm planning to stay there for about 11 nights, say 5-6 nights on each side. I'd like to dive almost every day, maybe sometimes twice. Do multiple Cozumel wall dives, some night dives, Cenotes at least once or twice, but also visit Chitzen Itza, whatever other non-marine attractions that region has to offer, experience some local culture, some night life. Given my interest in diving, I'd probably want to spend most of my mornings in Coz.
One option seems to be to fly to Cancun (non-stop flight), get some kind of local transportation to Cozumel, stay there for 5-6 days, get the ferry back to Playa, maybe then rent a car to do sightseeing, and spend the remaining days diving Cenotes and/or taking morning ferry to Cancun, to do more wall diving. Does it work? Also, how much pain will it be with one big and one small person dragging 4 heavy suitcases + 2 carry-ons? Is there some way to get all the way end-to-end from the Cancun airport to Coz hotels via van, or some such, to minimize inconvenience?
Another option, I don't know if better, would be to rent a car in Cancun, and travel over the car ferry. If we're spending 5-6 days on Cancun, this seems reasonable. Or not? Is the car ferry still running? I think I've seem some post claiming it's not.
Yet another option would be to fly to Coz, then fly back out of Cancun... flight to Coz take a few hours longer from where I live, not sure if this is really better than taking the ferry.
Other options? What would you suggest? Does the possibility of el Nortes somehow factor into the answer? How many days of el Nortes should we expect at the end of December during this visit? Do the Coz operators offer diving Cenotes as a backup if the port is closed? Or if not, is there enough time in the morning to take the ferry and hook up with an operator on the other side?
Stay in Cozumel - dive in Cozumel.
You only need 1 day to dive cenotes unless you really love them, then do 2 days or 3 days or whatever. You only need 1 day to see Chitzen Itza, actually only 1/2 a day if you leave early and get there before the mass of tourist swarm the place and bog you down. (key is to rent a car so you can come and go as you like and not be stuck on some God forsaken tour bus that is going to burn your whole day up) You can easily do Chitzen Itza and another ruin like Ek Balam or Coba or something else in 1 day if you rent a car and leave early.
If if was me and knowing what I know (which you don't have the privilege yet, as you've not been there) I'd
Fly into Cozumel
Spend 7 days diving butt off in Cozumel.
Take the people ferry across to Playa Del Carmen, rent a car and head south to stay in Akumal. On this day I'd check into my place in Akumal, chill a bit, grab some lunch by the beach, then head to Tulum to see the ruins, the awesome beach below the ruins, then head a little bit further south and have some beach time and dinner at one of the beach/micro eco hotels
Next day I'd dive the cenotes (actually I'd skip them, I've done them, they just kind of suck in my opinion, but some people do like them)
Next day head to Chitzen Itza early, very early, do Chitzen Itza and another ruin, chill, dinner... next day fly out of Cancun.
It's not my cup of tea to stay in Playa only to dive across at Cozumel, that's just not a good use of your vacation in my opinion, way too much logistics for the effort and results that will be lacking compared to the ease of staying in Coz and rolling out of bed and rolling into the water so easily as you can when you stay there.
Akumal is way better to stay at than PDC in my opinion. is closer to the things you want to do anyways. Rental car on the main land gives you freedom and saves you tons of time and frustration. Devote 1 day of diving the cenotes and see if you really like them. If you really love it, you can come back another time and dive them more. Exploring Akumal and Tulum is way more interesting and will yield great memories for the effort than hanging around PDC, unless you want kitchy shoping and night life, crowds, tourists... See Akumal and Tulum now, in 10 years they are going to be just like PDC. The growth south of Cancun is like wildfire, see what you can and experience what you can now while you can..
An alternative is to do it in reverse, fly into Cancun, get a rental car, drive down south, do the cenotes and ruins, then return the car and head across to Coz for 7 days, fly out of Coz or take the ferry across and stay a day and night in PDC then leave out of Cancun
I do it all the time! 
