Judo is the sport side of Ju Jitsu. It was thought that Ju Jitsu was too deadly to use as a competetive sport, so all the nasty bits were taken out and it became judo. Though now it has become competetive, with a lot of MMA cage fighters training in ju jitsu.
I have trained in judo, aikido, ju-jitsu and karate and they all have their good points. They also have their weak points, especially in a self defense situation. In my opinion in a confrontation a knowledge of karate would be best. The only contact with an aggressor is a foot or fist in his face.
As for karate being nothing but dance, that is so wrong. You have seen the katas and think that's it. You have no comprehension of what the katas are for, there are plenty of karate students who don't understand them. Karate is a very strong martial art, the body has to be conditioned more than any of the other three. You can only go through this if you have a very strong spirit that's why so many never make it to black belt. I have two students, aged 13 and 14 going for their black belts in a few weeks, they get hit with bare knuckles. Outside the dojo, we'd be arrested for the way they get 'beaten'. But out on the street they are more prepared than the majority of kids, a punch of a thuggie is not such a problem when you condition yourself to pain.
I teach my students karate and ju jitsu, and in my opinion the best way for kids is to start with karate for a few years to understand the dynamics of kicks and strikes, then start ju jitsu when they are more able to understand the complexities of the art. Also for kids, the repetative way of being taught karate is better and easier than the flexible system in ju jitsu.