I think Jake hit a significant point which is that the rules do affect the outcome of a competition, depending on the skills that the individual brings in with him.
Check out this thread on evolution of the rules and ring strategy: http://www.bladeforums.com/ubb/Forum6/HTML/001330.html
I think talking about the competition ring is one thing. Talking about a self-defense scenario is another. I am not sure we can conclusively say BJJ is superior to traditional JJ in the latter regard. Too many uncontrolable factors in the latter regard. For example, in Van's forum, David E raised the issue of a "grandmother with a broom stick" beating up an empty hand "master" after a year of training. Actually, this was the perspective of the late Donn Draegar who frowned upon "modern Budo" and "competitions" as not representing true "jutsu." For him jujutsu will always be about combat and combat means utilizing whatever it takes to win, including weapons. Draegar was himself a high level judo player and aikido practitioner, but his love of the "traditional" arts focused on Koryu -- old systems that emphasized weaponry over the "minor" empty hand arts.
Going back to BJJ vs. JJ. It should be acknowledged that the Gracie Family demonstrated a very successful training program for "competition" and their approach certainly emphasized mastery of technique over brute strength. I also don't doubt the competition skills can carry over to certain street situations as well but as one of the Gracie brothers wrote in a Black Belt article, it's not practical to go to the ground with more than one BG. Of couse, likewise, it wouldn't be practical for many of the "empty hand" artists either.
As the link above indicated, there is an evolution of skills and cross training in the mixed martial arts competitions. It's almost hard to differentiate grapplers from the strikers these days because each will focus some training in arts other than what they specialized in. I haven't watched much of the recent competitions. Yet, I did notice a evolution of even in Royce Gracie's fights from early in the UFC to when he retired. In his initial fight, Royce Gracie demonstrated no striking skills at all. Towards the end, you can see the improvement and the training that probably went into it. He had too. The competition created more and more mixed skilled opponents.