The diiference is in practice!
The difference is mainly in how they practice and conduct a class. BJJ schools aren't family fun centers like most places where martial arts are taught these days. You won't find out of control kids, soccer moms, or Bruce Lee wannabes in BJJ or MMA schools.
To be more specific about how it differs from Japanese juijitsu...
Brazilian Jujitsu is actually more of an offshoot from Judo than it is from Juijitsu. A judo master by the name of Meada taught the Gracie family his style of Judo and the Gracies adapted it even further into an almost all grappling system.
I think the most obvious difference in Brazilian jujitsu versus Japanese styles of juijitsu are the way in which they practice. Brazilian jujitsu is sparring intensive. They emphasize submission grappling, not katas,or throws, or kicks, or even hand strikes. Since they concentrate so much of their efforts into mastering and practicing submission grappling they are simply the most technically sound at it. Japanese jujitsu schools show you same things and even throw in some weapons training and striking technique, but they usually can't hold a candle to BJJ practicioners on the ground. BJJ is also definitely less of an art than is Japanese Juijitsu. BJJ is more of a street fighting system and as such is considered the "dirtiest" form of jujitsu you can learn.
If it were me I would choose BJJ over JJJ. I think it's definitely more suited for today's environment than is JJJ. And if you don't believe me just pick up any UFC video with Royce Gracie in it or perhaps a Pride video with Rickson Gracie.
I hope that helps you out some.