Cost aside, the double is a very specialized tool, and while a specialized tool can perform a number of tasks, it cannot perform tasks other than it's primary task, as well as a tool designed to perform in a more general role. Few clients go to Africa to hunt only one type of game, and by far the majority of clients book 7-10 day hunts and bring a single rifle. For this reason the double is without a peer as the professional's rifle, but the turnbolt magazine rifle is without a peer as the clients.
So if the bolt gun is the best choice, the question is then to choose between a push feed or controlled round feed rifle. The Weatherby Mk-V Dangerous Game Rifle is perhaps the best feeding rifle available due to it's straight line magazine, and it's a push feed. That being said, it's hard to ignore the points made by Mauser98. When it comes to choosing a rifle for dangerous game either system should work considering the cost of the rifles. A properly built rifle suitable for this type of work should cost about $4000.00 - without glass. If you have not paid this much for your big boomer, chances are you've missed some important details. A M-700 out of the Remington Custom Shop should work, but it wouldn't be my first choice.