Hi there!
My wife and I did the deep water swim last April on our Nassau day. The scooters aren't used the entire time, no.
We were provided wet suits and snorkel gear and instructed to meet in a room where we met with a guide (or dive master... whatever he was called). We were given some basic instructions and then brought out to the swim area.
We split up into two groups and while one swam with the dolphins, the other was pushed across the lagoon on a boogie board by the dolphins. The swimming was holding onto a power scooter and following the dolphin across the lagoon. Afterwards, we were able to kiss the dolphin we swam with.
It was really a wonderful experience. It's sort of misleading in that you don't get to 'swim' with the dolphins as you see on TV... but I wouldn't hesitate to go back if my wife was so inclined.
After the experience, you have the opportunity to purchase a photo package... and then you also get to explore the grounds of Atlantis, which was nice.
Overall... I'd certainly suggest it to anybody. How it compares to the shallow water experience, I'm not entirely sure.
Either way you go... HAVE FUN!
CY