Both agile and waterfall methods attempt to give you a pattern by which you can predict when software will be delivered. That's the main business value. The suits don't care how the devs operate, provided they can get things on time.
Waterfall tried to do this by trying to understand the problem as fully as possible, to liken it as much to previously solved problems, and to involve gurus to say "that kind of problem will take X amount of time to resolve", and thereby create milestones and delivery dates.
Agile instead said "look, we don't know enough at the start of a project to do that. Let's instead keep track of everything we want to do. Let's try and estimate each set of tasks (stories), individually. And then let's rank them in priority. We can measure how good our estimates are, we can modify them, we can generate more data and determine what we'll have at a milestone, and then can either push back the due date, or at least recognize that we won't be able to ship the entire feature set at that time.
Continuous delivery can be done with either one of those (it almost never is in waterfall, but it -could- be). But by itself it offers a business nothing for planning purposes. All it does is allow an immediacy, a "as soon as it's done it's out in front of the users". This may or may not be a good thing to the business, but it doesn't solve the basic issue that business people want to know when they can expect a given set of features to be live.