I'm familiar with the basics of Krav Maga (history, philosophy and approach), but not a practitioner. There's a lot to like in this martial art from my perspective, but I generally don't see any mention of a competitive/sports aspect of the art - in fact, I generally hear practitioners specifically promote how Krav Maga is not sports-oriented. All of this got me to wondering, is there a sports-oriented version/aspect of Krav Maga? And if so, how does it differ from the more self-defense oriented Krav Maga practice?
First, Krav Maga doesn't refer to itself as a martial arts. It's more appropriately called "Self defense tactics system." This might seem like marketing fluff, but the idea is that there is no art to it, and it want's to separate itself from traditional martial arts.
Second, there is no sports (also known as competitive) aspect to Krav Maga. Krav Maga itself takes it's learnings from many martial arts: Boxing, Tae Kwon Do, BJJ, Muay Thai etc, which do have competition and rules, but eschews them for a simplified fighting style.
If you want Krav Maga with a competitive nature to it, then I recommend MMA, which has a lot of overlap with krav maga, minus the weapon defense, small joint manipulation, and other "hurt at all cost" moves (eyepokes, ball-kicks, etc), which are generally illegal in competitive martial arts.
Krav Maga has no competitive aspect, as the rules of competitive fighting would be incompatible with many techniques, but to answer your question, the Krav Maga taught to civilians around the world is the sports-oriented version of Krav Maga.
There's a lot of marketing rhetoric about how deadly and effective Krav Maga is, and practitioners and instructors will tell you that Krav Maga is not a martial art but a self-defense system, blah, blah, blah, but you should keep in mind that the Krav Maga taught to Israeli Special Forces is not the same thing that instructors around the world teach to civilians.
People are right when they say Krav Maga is deadly and intended to quickly incapacitate the opponent by causing serious injury or death, but most of the time an instructor teaching Krav Maga to civilians won't teach many details that set up the conditions for causing serious injury or death to an opponent. This is simply because civilians learning Krav Maga for the sake of self-defense won't need to kill an attacker with their bare hands in order to defend themselves, and there's a good chance they will go to jail if they do that. That kind of legal trouble associated with the name will bring the kind of bad reputation that no contract disclaimer or public relations effort can prevent.
As far as I know there has been one tournament held last year by the Israeli Self Defense Force. The scarcity for competition in this field are likely due to it's brutality. Krav Maga leaves the opponent damaged and crippled through the use of eye gouging, groin, and throat shots. It was created for the purpose of self preservation and many of the techniques would be unsafe and unethical to preform for sport.
I took Krav Maga for about a year with two different organizations. It can teach you to defend rather quickly and get you to safety in a B- line. But to say it teaches to kill is over kill. Any martial art can teach you to kill, but going to jail is not worth it. Once the adversary is on the ground leave the scene—hitting more than that will get you locked up for too much force. I like the bursting concept of it, to many choke escapes. One or two will do but to go thru your mind selecting out of 12 is useless under stress. The knife blocks are even worse, very dangerous. Use objects around you to defend against a knife and any other weapon.
user1592 is right. Imagine someone who knew KM just walked into an MMA cage and started fighting. KM practitioners are trained to kill right? They probably would most commonly seriously injure someone every time they entered the ring. If you ask someone who is an expert on KM, they'll say they know a gazillion ways to kill someone. That's not okay to put in a competition, even MMA. I've even talked to someone who has just a few years to get to intermediate KM. Guess what? He knows a couple hundred ways to kill that are ONLY to be used IN SELF DEFENSE.
I'll cite some sources of the most lethal martial arts and you can read about the top few. You'll notice KM is usually 1st place, at the end, on the list. These lists tend to count down.
I know your probably thinking "duh" after reading some of those links. Maybe everything said on some of those isn't the most reliable, but reliable or no they all say KM is the most deadly. The reason is because its simply for serious self defense and involves some serious techniques that probably will kill the person they are performed on. The real purpose of KM is probably more likely to be used if someone has a knife or a gun and threatens you, not for MA competition.