Agile and Waterfall oppose each other. Therefore, the worst is to mix them into one project. Unless you have created your own hybrid methodology after sufficient testing and validation in your living organization, do not consider using it.
Agile fits better into contracts that allow incremental deliveries and once good communication between business and engineering staff can be implemented. This is often found in innovation efforts, software development, and startups. Waterfall works well for building products that can be described in detail earlier, at the design stage, and as long as you don't anticipate major changes to the products over the duration of your project.
In Waterfall, project success is more about getting lower costs, higher quality and meeting tight deadlines. In Agile, success is measured by the value you really deliver and, most importantly, by how much you learned during the project, in order to make improvements to your product that actually contributed to raise your customer response rates.
PMs must understand both methodologies so that they can make a decision on which one to apply depending on each scenario.