I did a great white cage dive in SA on a trip a couple of months ago..so I can give you some info that I either found on while looking into it myself or from just in conversation with the operator and other passengers on my trip--hopefully all correct but it's not as if I'm a local... I did mine out of Gansbaai, one of two choices to go from, the other being False Bay. From what I was told, False Bay is generally considered better for viewing "predation," including breaching which you mention, while Gansbaai might offer a better overall chance of encounters and had a bigger population of great whites. For False Bay/predation type trips, a South African friend highly recommended apexpredators (
www.apexpredators.com), but since I did mine out of Gansbaai I arranged mine through Pisces Divers (
www.piscesdivers.co.za). They in turn used another company whose name I can't remember...but if you talk to Pisces they can set you up through them. I would really recommend them...we saw 3 different great whites on a day when other boats came back seeing nothing..I also had a friend go a couple of weeks later with someone else and he saw nothing as well..apparently the experience of the captain and crew make a big difference. You can have the option of including transport to/from Capetown (about 2 hours away) if you don't have your own transport or prefer to stay out there.
A couple of words about the "dive"---you'll see it couldn't be further than an actual dive. The cage is attached to the side of the boat and you get in with probably four other people and stand shoulder to shoulder so that the water is probably chest deep. When a shark approaches there are lures of a bag of fish heads and of a small seal that are then maneuvered around to try to get the shark to surface/breach and to get as close to the cage as possible. When the shark is near the cage someone on board will shout out something like "shark right" and you'll pull yourself underwater and hold your breath and look. It's all rather hectic, vis typically isn't very good, and it's very hard to take photos..but we got great close, literally "you could reach out and touch" type views. You additionally got great views from the boat of the sharks at the surface. As you probably know, the water is incredibly cold around CT..count on 15 degrees and less! I really don't think that anyone offers any type of trip without a cage.
But definitely worth it..fantastic experience..here's a pic from when i went.