Having a lot of experience in the Waterfall approach to software development, I thoroughly enjoy how Agile Scrum "cuts to the chase". That is, we deliver meaningful results to our clients far sooner than with the classic BUFD's - Big Up Front Documents - where the clients can wait months, perhaps years to see a solution implemented.
One of my projects involved moving an older application to a more stable, robust and secure enterprise platform. Lacking documentation for the current system, I analyzed and "decomposed" the application's elements - its database, tables, UI's, functionality, data flows, inputs, outputs, reports, stakeholder & user identification, workflow analysis, etc.
I then translated the new functionality into user stories, working with the development team to create and test the new system. We also participated in daily standups, story grooming, prioritization, sizing and other Scrum activites.
In writing our user stories, we were guided by the I.N.V.E.S.T. principles of Independent, Negotiable, Valuable, Estimatable, Scalable & Testable.
Although some solutions will still require a Waterfall approach, I'm an advocate for Agile Scrum wherever we can encourage and support an organization's adopting it.