I trained Krav Maga for two years and its really cool because you cut to the chase and start learning useful stuff from the first day.
Imi Lichtenfeld created the system around the 40's to teach jewish people to defend themselves, so it needed to be brutal and easy to learn (Check this
http://en.wikipedia.org/wiki/Imi_Lichtenfeld)
I like the way KM is taught with heavy emphasis on stress and multiple assailants, all strikes are directed to vital areas being balls, eyes, throat or nose.
Some people criticizes that the techniques are scripted, and real life isn't, but with practice you assimilate the technique and become able to adapt to the changes.
What I DIDN'T liked about it, is that it focus too much on defending attacks, but it never teach you how to be the attacker.
For sure you'll spend a lot of calories in the class, I always finished soaking wet.
About jiu jitsu:
I wouldn't choose it because its all about grappling and fighting in the ground and in a real fight you go to the floor and you're dead.
Here are some examples...
While you are on guard on the floor, a friend of your attacker will stomp your head to death, or hit you with a knife in the ribs or your enemy will bite your face/ears off.
Ground fighting is important, but you shouldn't rely on it as default, always stay on your feet, movement is key.
I enjoy MMA matches, but that doesn't represents a fight in the street, that's just a show with tons of rules and protections.
Good luck in your class NOLA, and keep us posted to see how it works for you