What makes a good beat 'em up? Well, let's see:
1) Good controls. So you need a good format for them. Personally I'd go with about 7 buttons needed for a good modern day beat 'em up. I'll give you an example of them:
f) Grab - Nothing is worse in a beat 'em up where you accidentally grab when you meant to punch or kick. Intentional grabs are always good if you don't have a good system where you grab. SoR for instance has a good one, but say the classic Double Dragon? Not so much. This can also be used to stop the general confusion games have with attacking versus picking up a weapon. Now there can never be a moment where the player can attack the enemy
g) Back Attack - Because it's annoying to have it mapped on dual buttons.
The biggest thing that kills beat 'em ups for me is when you have limited controls and those are half the reason the game is hard.
For varied enemies, I'd say the big thing is to have something in mind for the enemies. For instance, take Streets of Rage, every enemy pretty much has some "specialty." Galza's throw you and do sliding tackles to knock you on the ground, Donovans are anti-aerial so jump attacks are less useful, ninjas land on their feet when you throw them and also have projectiles, boxers can block so throwing them is the best option against them... The biggest challenge is trying to exploit these patterns in various environments and various enemy formations. That's what makes it fun. The problem with so many beat em' ups is that the enemies you fight have no real rhyme or reason to how you fight them (or how they fight for that matter), so when you encounter another enemy you just approach it as a new punching bag.