There's really no comparison, as they're completely different types of programs.
Dolphins in Depth is, to my understanding, your standard dolphin wade/interaction program common to most institutions. Pet them, feed them, stand in the water for a couple photo ops (hug, kiss, etc). It's going to be quite similar to the actual dolphin swim portion at DC, although I'm not sure if Dolphins in Depth has the quick deep water tow portion that DC does. Maybe someone else could clarify that.
For DiveQuest, you'll have to be scuba certified to participate. My instructor works there as a DM, actually. It's supposed to be a pretty fun experience, even if not as exciting as actual ocean diving. I'll be doing this program in a couple of weeks. They gear you up (so don't bother bringing anything other than your mask) and let ya in the tank for about 45min to an hour. Fish, sea turtles, and a couple of sharks.
Never done AquaQuest, but I assume it's a tour of their area. Might be interesting, but I have no idea what it entails.
Discovery Cove, however, is an entirely different sort of experience. It's more like a day of immersion in a tropical resort. The theming is incredible and the whole day is very relaxed. The service is impeccable. Once you get in there, everything you need to enjoy your day is free... towels, lockers, wetsuits, snorkels & masks... even your lunch and snacks are free! (And the food is pretty durn good, I think!) All you'll have to pay for are souvenirs and photos taken by the staff (except for the photo they take of your group on the entry path.. that one's comp).
The dolphin swim portion is done in a group of about 5-7 people. You'll do the standard dolphin swim things.... again, petting, feeding, photo op poses, a few tricks.. and you'll generally do a (admittedly slow) dorsal pull back to shore. It's a good experience.
They also have a "lazy river"... freshwater, heated. It starts at the resort pool and wanders through waterfalls and pretty scenery until it goes into their free flight aviary. There are three aviary sections where you can feed the birds. (You can also access this via a door behind the stingray pool if you want to visit without swimming through the river.)
Then there are the two saltwater pools... one is their reef pool, which is about 12-15' deep and full of tropical fish, southern stingrays (on the bottom), and spotted eagle rays (midwater swimmers). Behind a glass wall under the water, you can see barracudas and sharks swimming in the adjacent tank.
Next to that is the stingray pool. About 3-4 foot deep, you wade in (make sure you shuffle your feet to avoid stepping on any buried rays!) and can pet and feed the cownose rays and southern stingrays (all with tail barbs safely removed). It's really amazing... they're very graceful and swim gently around you. One of my favorite parts of the park!
All of that is included in one price at DC. No extra charge for the animal food or the stingray pool, or anything.
Personally, I can't recommend Discovery Cove enough! Yes, I might be slightly biased as I worked there for a while... but I've been as a guest six or seven times now since they opened... and I'm looking to go again this summer! I definitely think it's worth it. Really is a one of a kind experience!
=)