drama drama drama... character build up... build up of power between the two characters.. build up of rivalry (falls under drama)... build up of motivation

and of course the second element is good game play quality, what yuo can do, how you can beat them up, the level of skill involved, the difficulty...

(can you use weapons, where do you aquire them from, off your fallen foes, stores, off the ground randomly.. etc... since it's mostly beat'em up, you can just have a basic increase in range of attack, and damage increase for each weapon.)

Maybe even have clothing that chagnes the look of your character, but doesnt' add stats (that might make it to much of a strategy game), or the stats are really straight foreward, everything increases attack damage, some more some less.

Depending what type of beat'em up game, you ca borrow some ideas from river city ransom, wher you had level up of various stats.... could learn new fighting techniques, perhaps efffect how high your charcter could jump, or if hitting differnt body parts could do more damage.

Maybe you could add in a move that stuns an opponent, but can only be used once, adn stop whatever move the opponent was about to do (Assuming it's not turn based), the reason you can make it only usable once on a foe, is because if you make it reusable it becomes an issue to contemplate abuse of the move.. Should you give the move diminishing return, make it have a time period before yuo can use it again, (it again complicates the game, and gives it a more strategy feel, not to say a beat'em up game, can't have any strategy in it, just generalyl that's not the focus of the game.)

Also Decent enough grapic quality to not distract from the game, and can make whatever sttyle of gameplay you want beleivable... if you say do a slash with a sword, don't have horrible graphics of them donig a slash, we want it so that you can tell by some way that he actually slash him with a sword, whether it hit, missed, or was blocked, other than potentially paying attention to hp bars.

Maybe hyou can make it more realistic and don't use hp bars, maybe you do some status text, like it pops up (so and so cough up blood), which means to the careful observer, whose noticed what happens everytime that line appear, that that particular foe is loe on health. (if the graphcis are good enough maybe you could have the person holding there stomach when they low on health, or various other things...)