The real question isn't which one is modern — it's where in the project the requirements are still allowed to change, and what that costs to allow.
Waterfall is a predictive, sequential life cycle: requirements are gathered and locked, then design, then build, then test, then deploy — each phase gated by formal sign-off before the next begins, with changes to earlier phases handled through a formal change-control process. Agile is an adaptive, iterative life cycle: the team builds working increments in short cycles (sprints), gets real feedback after each one, and deliberately keeps scope open to change based on what that feedback reveals. Neither is inherently "better engineering" — the right choice depends on how well the requirements can actually be known up front, and how expensive a late-discovered change would be to absorb.