The most significant change is that Agile Project Management is just that: agile, non-rigid, flexible (does that scream scope creep?). There is value in both the Waterfall and Agile methodologies, and knowing when to use which method is a key to success.
The best advice is project manage your project management! Waterfall is perfect for projects that have low variability, low complexity and few unknowns. Construction and repeatable work fit best with the Waterfall approach. In contrast, Agile works best when complexity and uncertainty is high.
Agile provides high visibility, lots of inspection points and the ability to change the scope based on status. Agile affords constant feedback and checkpoints to make sure you are on track, allowing you to define the uncertainty as you go.
As a Project Manager, your process changes, your team structure changes and your lifecycle changes. Rather than focusing on the planning (as with the traditional model), Agile Project Management focuses more on the execution phase. The triple constraint is replaced with meeting business objectives and speed to market. Agile welcomes in high bandwidth of communication and active problem solving, which helps to find defects right away.
So be adaptable, select the right approach and enjoy success!