Secret World Legends has a system similar to this where the base dungeon is considered the "story mode" and then there are Elite 1-9 versions of that dungeon that progressively scale upward in difficulty. Elite 1 is only slightly more difficult than story mode, while 9 is like a step above savage, where few players ever go. I think Elite 6 is where you start seeing different or more aggressive mechanics. Each tier has a minimum level requirement.
The rewards scale up with each difficulty tier. In SWL, gear is upgraded through melding (adding xp to a piece of gear), and each tier gives higher concentrations of these distillates. Once you reach certain intervals, you get new gear drops with special effects that are attainable from boss kills.
The biggest reason for trying to complete all tiers is achievements that reward vanity items, pets and titles.
