From your comments I’m assuming that you haven’t actually watched any MMA - that is, Pride, UFC, WEC or the like.
The reason I say this is because the very purpose of the sport’s creation was to answer this very question. Royce Gracie was a practitioner of a relatively obscure martial art - Brazilian Jiu Jitsu. BJJ is a more practical, pragmatic modification of the original Japanese version; you can look up youtube videos of various Gracies challenging esteemed members of various martial arts to full-contact fights. They almost invariably end up the same way - a takedown, a mount, punches in the face until the karate/judo/tae kwon do/etc master rolls over, and a coup de grace via lionkiller. Most traditional martial arts focus a single aspect - striking. Very few have groundwork of any kind, let alone any way to defend against the movement-denying grappling style of BJJ.
So, anyways, Royce Gracie wants to prove the superiority of his martial art. He starts the Ultimate Fighting Championship, a come-all-takers Dragon-Ball-Z style fighting tournament. Aside from restrictions on eye-gouging and fish-hooking, there were no gloves, no rules and no time limits. Opponents fought until one was rendered incapacitated or submitted. It was a pretty brutal scene as evidenced by the infamous first fight (starts at 5:00, violent).
But you wanted a one-on-one comparison of the martial arts, and that’s precisely what UFC1 represented. A few things became quickly clear through the course of the evening: other than a brawler push-them-down-and-kick-them-in-the-head barfight technique, martial arts that lack a grappling component are virtually useless against those that do. Judo, Jiu Jitsu and wrestling practitioners were by far the most successful. Unsurprisingly, Royce Gracie won while wearing a full gi, the uniform of his martial art and a huge liability in a fight. So, to answer your second question first: assuming your opponent doesn’t have friends to kick you in the head once you’re on the ground, a reasonably skilled BJJ practitioner should be able to subdue most average Joes in short order. Nobody likes getting punched in the face, and a decent rear naked choke can render one unconscious in under ten seconds.
Since then the mixed-martial-art scene has really become, well, mixed. Gone are the single-discipline styles of fighers - there are no more ‘karate master versus kickboxing expert’ matchups. Instead most successful fighters combine several techniques from numerous fields. Generally you will see; striking arts in boxing and muay thai, grappling techniques from both greco-roman and collegiate wrestling and textbook brazilian jiu jitsu techniques. Given the enormous amount of money floating through the sport right now, you can be assured that they’re plucking the most effective martial arts from the bin; but only to fit the rules of that situation. This is where most MMA-street fight comparisons fall apart - however given your thunderdome-style scenario I’d put overwhelming odds on the average MMA musclehead over any equivalently skilled “martial artist.”
Krav Maga may very well be the most effective, overall, since it emphasizes killing that motherfucker with the bottle on the bar or kicking his testicles in and soccer-kicking them in the throat once they’re down and running away the moment they stop moving. But unless Krav Maga training involves actually getting punched in the face (and I’m truly ignorant on that subject) I expect they’d react similarly to most purists when getting jabbed in the nose and give up a takedown in short order.
On the ground, BJJ is king. And fights always end up on the ground. And people who snicker during grappling combat are completely ignorant. IMHO, of course.