I have Verizon, you can either pay per day like if staying a week or when I stayed a month, I turned on international for 25 bucks - 500 minutes, unlimited texts and 1gig if I remember right. I used the net for data if I needed it.
I thought the 25 bucks just got you the ability to access your regular data and call plan. I didn't realize it had separate limits.
Keep in mind, if you've got a "business" plan for your phone then the costs to roam internationally are very different.
Using a US based phone in Cozumel has a couple benefits.
1. People can reach you at your normal number
2. You can reach people back in the states without doing anything special (just dial the regular number)
The main drawbacks that I can think of are
1. Cost
2. dialing a dive shop or hotel or other business or person in Mexico might require international dialing. It's not a huge deal once you know what to do.
Buying a burner phone or just a Mexican SIM card has different benefits.
1. Calling businesses/people in Mexico will probably be easier (your hotel, the dive shop, etc).
2. Cost
the main drawbacks that I can think of are
1. Dialing US based numbers (such as a dive buddy staying in another room) might require international dialing.
2. Burner might not include international calling without an extra fee.
3. People have to know the number of your burner in order to reach you.
4. If you take pics with your burner phone, you'll probably want to transfer them to your regular phone eventually. (not an issue if you just got a SIM for your regular device)
5. Unless you're using android for both the burner and your regular phone you probably won't have your contact list on the burner. If you're using android, it will just synch up once you setup the burner with your google id.
That's all I can think of. There's sure been a lot of threads on this topic. It's probably worth searching the Cozumel forum on Scubaboard for more info.