I got this idea from the Master Chief vs. Solid Snake thread.  I'm sure something like this has been done before, but what the heck, I'm bored.

Tell me, Who would win the fight, how he would win and why.

I'll go first (duh!)

Luigi - Why?  This is no ordinary Luigi.  He's the Luigi from Mario Is Missing.  And for those who may not know,  this Luigi can NOT die. 

Next.

I'd say Luigi because he can jump higher. Traditionally jumping on the head is the biggest attack in the Mushroom Kingdom. So higher jump is the advantage.

I suppose I'm going to go too in depth into this but here we go....

Looking into the history of the Mario Characters, Mario is traditionally suppose to take on the 'hero' role. With it, his personality is more of a driven character who is more focused on his end goal and not of his surroundings. In this way, the argument could be made that, while he isn't dumb, Mario has a one track Mind, as many Heroes do. Which often can be a handicap.

Luigi on the other hand passes off as timid, reluctant and altogether 'weak'. But is this really the case? Its clearly been stated by Nintendo that Luigi is not only smart, but 'devious'. And he has at times been provoked to display what seems to be close to a dual personality. One of his scared self who is willing to allow himself to stay a sidekick to his brother to avoid danger...and another who welcomes danger and becomes nearly as strong or stronger than his brother.

Anyway....the in depth analysis of the Mario Bros aside.....I'd say Luigi. Just because if you took both the move sets for Mario and Luigi from Smash Bros, put them into a game like New Super Mario Bros, I believe Luigi would come out as the more versatile one.