The biggest challenge with a waterfall approach is that it delays risk resolution and makes a large number of assumptions regarding just how complete and accurate the project's requirements are and how well the team will be able to deploy a solution in the required timeframe.
Scope creep
The value of an iterative and incremental approach is the recogntion that everything is NOT known up front, that the requirements will evolve as the business stakeholders and the project team get to grips with the required solution and that the ability to deploy the solution will test the capabilities of the business stakeholders, the project team and those responsible for the technical environment.
Scope is frequently challenged early in the development process and yet schedule and cost will have been fixed and challenges come down to a question of cost, schedule or functionality... the core value proposition of an iterative approach is that any one of these elements can be assigned priority over the other and choices made earlier in the project as opposed to later.
Allowing visibility of the challenges early and the provision of a mechanism to manage the challenges to initial scope and allow business and technical stakeholders to resolve conflicts in priorities of functionality enables early and proactive management of scope issues and decisions.
Risk resolution
Risks in projects take many forms, aside from questions of scope these extend to the solution actually performing in a production environment. Past experience in projects has shown that technical risk is frequently carried late into the development lifecycle and often only becomes visible just before deployment into a production environment... way too late for any proactive managment and response.
Worse yet, these issues may only become visible once in production.
Early determination of performance issues through performance testing of key architectural components resolves risk early in the project lifecycle and provides a stable base for development.
Long story, short...
The value of a project team (including business stakeholders) stepping through the development process in small increments and proving a deployable solution provides significant value and confidence when delivering a long term project.

