I got started in Krav Maga recently, after having spent some time in a well-regarded MMA organization. First I'll say that I am far from an expert in either.
My impression is that it's not exactly an apples to apples comparison. The primary goal of Krav is to kill/maim/immobilize or render impotent an attacker in a situation where your life is on the line. It is truly a "no holds barred" situation, while in MMA, it's obviously different. There are lots of rules in MMA that prevent a Krav practitioner from using some of his primary weapons-- gouging, scratching, biting, head-butts, joint locks, vertical elbows, etc.
There is also the issue of physical conditioning. I've found so far that the Krav methods are not nearly as physically demanding as MMA in that they don't spend a lot of time on strength training or long-interval cardio, like an MMA fighter. The goal in Krav is to stop the fight as soon as possible, however possible, and they wouldn't be trained for several 3-5 minute exchanges with an equally fit opponent. Most real-world street fights will probably never last more than a minute at most. From a power standpoint, there could also be a disparity. Punching and kicking techniques are primary weapons in MMA, and the intense strength and cardio training they endure helps the MMA fighter to put as much power as possible into those techniques. While important in Krav, punching and kicking are complimented by all sorts of other "strikes of opportunity" so that the weaker defender is at less of a disadvantage when facing an opponent who has greater size and strength.
I would imagine that ultimately, the MMA fighter would have the advantage in the ring and a well-skilled Krav practitioner might have the advantage on the street. Even still, it is primarly useful against attackers with little or no combat training or those with training who don't have a considerable size and strength advantage. I do think it is true that in any situation and in any discipline where you face an attacker who has both effective combat training as well as size and strength advantages, you are probably going to lose. Put a soldier (unarmed, of course) with average to above-average physique who is an expert Krav Maga fighter against a world class MMA fighter with an extreme physique, and my money is on the MMA fighter 8 out of 10 times.