Whether viewing websites or MMA, Judo, and BJJ forums, the subject of Judo vs. BJJ has become yet another classic debate, akin to that of the old "Gi vs. No Gi" debate. However, the question of Judo vs. BJJ is much simpler to answer because it is simply the wrong question in almost every applicable context. In short, an Olympic level Judoka would benefit from Brazilian Jiu-Jitsu as much as a world-class BJJ player would benefit from Judo.
And at the top level, there are multiple examples of this beginning to happen. GB's Winston Gordon trains with Gracie Barra and holds a purple belt in Brazilian Jiu-Jitsu. Ray Stevens, former Olympic silver medallist, has been known to train with Roger Gracie. Dave Camarillo, Rhadi Ferguson, and Lloyd Irvin have become vocal advocates of cross-training these arts and have all enjoyed considerable success in both sports. Therefore the answer is Judo AND BJJ. Most top level players are starting to know this fact and rarely ever involve themselves in the nonsense of the forums.
However, trawl the forums and you will frequently see this very discussion taking place. Comments range from the petty such as a "judoka" commenting about BJJ players wearing too many patches on their Gi's to the erroneous "BJJ player" commenting that "judoka's are easy to double leg". I also recently read from one judoka that "either never seen anyone in BJJ show me a move that didn't exist in Judo".
Such comments are harmful because they slow our progression to be the best that we can be. It is a fact that within the "Gi sports" that the average Judo club will have a far higher degree of stand-up skill per person, and the average BJJ club (who out there thinks they are in an average club - Ha, that's another story and I'll be shot if I go there!!) will have a far higher degree of skill on the ground. Assuming that the respective coaching levels are held constant then anyone wishing to balance their skills would surely want to practise stand-up at the Judo club and BJJ at the BJJ club. And this is why comments such as "I've never seen anyone in BJJ show me a move that didn't exist in Judo" are so unhelpful and completely miss the point. Neither art is really about knowing the greatest number of "moves" and anyone who has trained in the competitive environment knows this is the case. However, such comments promote ignorance and division rather than learning and integration.
There are a multitude of benefits to training both Brazilian Jiu Jitsu and Judo, from greater all-round skills, to the cross-over benefits of learning different approaches to training (e.g. speed and power to slow and technical). There are simply too many to list here. However, anyone in doubt or uncertain should consider this: the learning curve in both arts is greatest at the beginning and therefore you stand the most to gain from the early days. When I first began Judo, I found that it was much easier to throw non-Judo players at BJJ. However, some months after, my BJJ friends began training Judo and learned to stiff-arm. All of sudden, I couldn't throw them as often (until I overcame the stiff-arm).