My family has done both of these, and thoroughly enjoyed them both. At Blue Lagoon we did not do the swim, but rather the encounter (I think that's what they call it.) With the swim you actually get in the water with them, and the dolphins push you at the end as you extend in a Superman pose. With the encounter you stand on a platform in water that is about knee deep, and the dolphins come up and you have a lot of interaction with them. The encounter is less expensive, and you really do get a lot of play with the dolphins (hugging, kissing, dancing, etc.) At Atlantis the dolphins are in a very large lagoon, and you stand in the shallow water at the edge of the lagoon. Then the dolphins come up to you, and you have similar interactions with them.
We found the main difference to be the sites themselves. Blue Lagoon is a quiet, private island, with a nice beach, inflatables in the water for kids to play on, hammocks, etc. You ride out to the island, which takes about 30 minutes or so. We probably preferred this site, because it does allow you to wind down a little bit after the mayhem of the ship. (Don't get me wrong, we love the ship, but at Blue Lagoon you can truly relax and feel like you're on a private island.) Atlantis is amazing, but huge. And depending upon what you pay for you either a) miss out on a big part of it or b) pay enough that you might have to take out a second mortgage.
You will get back in plenty of time from either site. At Blue Lagoon everyone there will very likely be from the Disney ship (Disney buys all of the spots when its ships are in dock at Nassau), and they have boats that return to the port at 1, 2, and 4. At Atlantis they have shuttles that returns to the port every so often, and they'll let you know on the ride over when the shuttle buses run. And you can always take a taxi back as well.
You really can't go wrong either way, and both dolphin interactions were incredible. So if you want some quiet time, go Blue Lagoon. If you want to see an incredible resort that is like it's own city, and have a little more flexibility in terms of when you can return to the ship, go Atlantis. Either way, you'll have a blast.