Hi Hudson69,
I think this has been covered a couple of times in different threads, but to concisely put it in one spot, here goes:
Essentially the main difference is in the emphasis of each organisation. The Bujinkan at present doesn't really look to teach the individual Ryu, or even the particular kata from each (depending on the individual instructor, of course), but rather it's emphasis is on the principles and nature of combat as expressed through the traditional teachings. There are various reasons for this, including Hatsumi Sensei's current belief's as to what is most important to keep these arts (and it's practitioners) alive. I might point out here that that does not necessarily mean that the techniques need always be "combat effective", as simply continuing to breathe is just a part of life, and is not the definition of being alive (or living).
Tanemura left the Bujinkan in the mid '80s (about '84 if memory serves) for a variety of reasons that we don't need to go into here, but he then formed his own organisation (the Genbukan) so he could continue to teach the arts as he saw best. The Genbukan's emphasis is on "correct transmission" of the traditional Japanese Martial Arts. As a result, there is a greater emphasis on physical standards and continuity in abilities across the board, as well as a greater emphasis on the technical aspects of the systems.
The Jinenkan was formed after Manaka Sensei left the Bujinkan in the mid '90's. The emphasis of the Jinenkan is on drilling the basics (as Manaka did with Hatsumi Sensei early on in his training), and then in teaching and learning the individual Ryu in the same order as the scrolls are written. Again, there is an emphasis on the technical aspects.
Each have their own particular strengths and weaknesses. The Bujinkan is great for getting principles, getting used to flow and adapting to movement, and will appeal to people wanting to be able to individualise the art to themselves. The downside is that there is less control over the end result, with gifted people gaining a very good degree of skill, but others being left floundering with little "solid" to grasp on to.
The Genbukan will get you very good from a technical standpoint, and has a huge base of knowledge to draw from. It's downside can be just that, though, with more information than you can realistically get through (for most people), resulting in an overload, giving a broad base, with little enough time given to mastery of any particular skill-set. A solution to this has been the traditional ranking in individual Ryu-ha.
The Jinenkan, with it's emphasis on the basics is one of the most solid bases in the Ninjutsu world. It also is the most limited in terms of schools taught, so there is more time to spend getting good at particular areas. However, with it's emphasis on the classical scrolls, there can be limited real-world violence (in terms of a street-style attacker) understanding, so from a strictly self defence standpoint, it can be a little lacking there.
Of course, these are generalisations, and good instructors (of which there are plenty in each organisation) will minimise (to the point of removing almost all) the limitations and weaknesses apparent, as well as heightening the strengths. And those are the instructors that will keep each of these organisations moving forward into the future.
