Have you ever worked with a stakeholder who revelled in being known as the busiest man in the office? Everything is an elevator pitch? They've seen it all.
How best to pitch the benefit of going agile over waterfall in less than 200 words?
I would turn your question around.
What is the problem your stakeholder is trying to solve?
Is it shortening time to delivery? Is it the ability rapidly adapt to change? Is it the efficiency of the delivery teams?
The agile approach is an answer to a question (or questions). It is not an end in itself. Work out what the stakeholders want and then evaluate if agile helps them get it.
I like to quote the book Scrum The Art of Doing Twice The Work In Half the Time:
Venture capital firms like OpenView Venture Partners in Boston, where I’m an adviser, say that Scrum offers too big a competitive advantage not to use it. These are not warm and fuzzy people; these are gimlet-eyed money men, and they simply say, “The results are indisputable. Companies have two choices: change or die.”
The mayor thing here is that if a competitor really starts working Agile (+XP practises) and builds disrupting technology or reimplement your product. They will keeps improving it in a very fast steady pace and not slow down until they have overtaken you.