We went to Cancun this past May and Riviera Maya in October with our young children. (In October, the boys were 3-1/2 and almost 2). We didn't leave the resort at all to go into town on either trip, so I can't really comment on how touristy one is versus the other.
We stayed at Moon Palace in Cancun, which is about 10mins away from the airport and an excellent resort. Reservations aren't required for any of the restaurants, so you can show up whenever you want and there aren't restrictions as to how many times you can go to the "nicer" restaurants.
In October, we stayed at Iberostar Paraiso Maya, which had a nicer beach but overall was not as nice as Moon Palace. (To be fair, I didn't realize Moon Palace is a luxury resort.) Smoking was allowed in outdoor public spaces (pool, beach), but I don't know if that's common or because Iberostar is based in Spain. It does have a lazy river, wave pool and playground onsite.