The correct answer to this open question is the following.
The Agile Manifesto principle that I am going to pick in the principle of "Embracing Change."
I think this is likely to have the biggest impact on the success or failure of a typical project in my organization because change is the constant in modern-day business. Probably, since the inception of the modern-day industry.
In order to be successful and maintain that success over the years -no matter the conditions- a company has to be ready not only to adapt to change but to change ahead of necessity. And this is one of the most difficult things to do in business because people love to be in a comfort zone for years. People in corporate America likes to know they are safe in their traditional places doing traditional things. For them, change is tough.
That is why I think "Embrace change" would be the principle that would help me the most.