We have done both - Nassau & Cozumel. I would recommend the Nassau Dolphin Encounters hands down. The facilty at Blue Lagoon Island is beautiful and very well kept, the water is many shades of blue. Cozumel's facility's were less then clean (I won't say anymore on that subject).
As for the encounter itself...in Nassau the actual area of the encounter is covered in a canopy. The platform that you stand on is not very deep (water was up to the waist on my 6 year old). There is no need to wear a life jacket. First they take each individual family into the water (the others are sitting around a rectangular frame (kinda looks like a mini pool). The famlity has their picture taken with the dolphin kissing one of the family members. After all of the families go through this process they take groups of 10 to stand on the platforn (again the others sit around the frame and watch). During this time the dolphins vistis each individual for a kiss (picture taken), dance(picture taken), feeding a small fish, touching his teeth and rubbing his back & tummy - all the while the trainer is talking about the dolphin behavior. He also does tricks - swimming on his back fins, jumping etc.
For the encounter in Cozumel...the groups (15-20) are led into the water on a platform. You must wear a life preserver and the water comes up to the upper chest of an adult. My husband had to hold our daughter as she was not tall enough to stand on the platform. Additionally the life vests make you very bouyant, it is difficult to stand still on the platform. You get to rub the dolphins tummy and back, give hime a kiss(picture taken), hold his fins. The dolphin also does tricks - swimming on his back fins, jumping etc.
Both are an incedible experience to visit with these fruendly creatures but the Nassau encounter really stands out as being exceptional.
FYI - we did the Cozumel encounter in 2004 and just returned from Nassau last week.
Have fun!