Let me outline the basic X kan differences and background in a few short paragraphs. This is hardly an in depth analysis, but enough to give you some understanding without losing myself in details and politics.
Bujinkan was the first formal ninpo organization, started by Hatsumi sensei, who was taught by Takamatsu sensei. Tanemura sensei and Manaka sensei were both students of Hatsumi sensei and eventually received menkyo kaiden in several traditional ryuha. Tanemura sensei already had other menkyo kaiden as well at that point, passed down via family lines.
At a certain point in time, Tanemura sensei resigned from Bujinkan, and sought out other former students of Takamatsu sensei. He continued studying under each of them while forming his own ninpo and jujutsu organization: Genbukan.
Some time later, Manaka sensei left as well, and formed Jinenkan.
These days, bujinkan does not teach a specific curriculum but focuses on prinicples and strategy (please correct me if this is inaccurate). There is no formal curriculum, and grading is not comparable with other systems. Afaik, it is also not possible to receive licensing in the individual ryuha that make up the bujinkan, at least not in general.
Genbukan teaches a formal curriculum, and students have to practise a set of techniques for each grade until they have those techniques down really well. Training and dojo etiquette are strict. At higher dan levels, student can earn licensing in individual ryuha, and are even required to do so in order to progress.
Jinenkan emphasises mastery of the basics. I don't know much specific about Jinenkan. I read in an interview with Manaka sensei that he will not grant anyone licensure in any of the older arts, but he might consider licensure in jinen ryu. I don't know how accurate that is though. It was an older article.
But with this all said, much depends on your teacher and whether you connect with him. If you feel at home and you get out of the practise what you are searching for, then it doesn't really matter which one you are a member of. Good luck.