Any project is a combination of 4 things: People, resources (budget, staff, software, licenses, technologies, etc ...), timelines, and deliverable set.

As the PM, you are tasked with plotting the best timeline for achieving the most deliverables using available resources and making sure all the people involved know it. That's it. Simple! Right?

The methodology itself is a guide - regardless which one. After all, no methodology is perfect. When it's all said and done, you will have to tailor whatever methodology to fit the business, culture, and expectations. Agile makes sense in IT because of constant change and difficulty in pinning down full specs ahead of time - so you want flexibility to rework and readjust mid process.

But I don't think this is what makes a sophisticated project manager.

Sure the tools and methods are important.

But I think that the most sophisticated project manager is one who can communicate with people best. And as such, ensures that everybody is on-board the change train all the time.