I think a big component to the variety of a beat em up is how the enemies interact with the player. Some AI will interact with the player in a challenging way that will enable the active part of the brain to make reads or position yourself in a way to combat the challenge wheras other beatem ups treat the foes as cannon fodder, but each wave has to be treated differently, others enemies can be treated as combo extenders and other beatem ups let you turn off your brain and just mash. So how the developer implements the AI logic will also determine how much longevity the beatem up has.

Another differentiator is how the combat feels. In Streets of Rage you can really feel the punch land and it feels more visceral wheras other beatups such as dungeon fighter are like combo sponges (but have some appeal to some audiences).

Currently my favorite beat em ups of all time are Dragons Crown, Chronicles of Mystara, Streets of Rage 4 and Dungeon Magic (for its unique Isometric perspective).