If your target is an old piece of hardware, beat 'em ups are actually way more complicated than 2D 1 on 1 fighting games to make.
They're more computationally expensive. Beat 'em ups like Final Fight are basically 3D games with 2D graphics. You have to handle X, Y, Z positioning, there are a lot more collisions/physics calculations involved if you want to allow for objects standing on top of each other, and there are more entities to handle than a 1 on 1 fighter. Fighting games have two real objects to handle at any given time. You can have 10-12 entities to handle in a beat 'em up, and the computer controlled ones will be wasting cycles on their AI.
In 1 on 1 fighting games, you don't even need a real collision or physics system for "levels." You can just cheat because there's a single "floor" without any varying height.
And on top of all of that, beat 'em ups tend to get less mileage out of them because they don't have as much replay value as a competitive game, so it's 1) more difficult to program 2) requires at least as many art assets as any other type of 2D game, and 3) you get less mileage out of what you make because what you end up with is something that can be completely beaten in under an hour.
There's a reason that people don't make a lot of them. They're probably the most complicated type of 2D game to make because they have all the development challenges of both platforming games (the level and collision challenges) and graphics showcase games (many large detailed graphics).