Technically there are no differences between these two organizations. The leader of both of these organizations are former Kyokushinkai seniors.
The founder of Kyokushinkai, Mas Oyama, passed away in April 26, 1994, but he did not name any successor. Therefore many of its seniors broke away from the original Kyokushinkai and each form their own organizations. There are close to 10 of such organizations now in the world.
If you just want to learn a martial art for self defense and not care about politic, any kyokushinkai are good but you must visit the schools and talk to the instructors to find out if they fit your need.
kyokushin karate, is very similar to Kickboxing and is very very brutal.
I say hands down the best think about it. its the closest thing to a real fight. self defense wise no the best
Both of those groups are very respected in the Kyokushin communties and events. There are probably about 12 others out there as well. The primary difference is that the Seibukai group is more focused on hard core, competitive Eishin style Sabaki events where as the Shinkyokushinkai is more focused on preservation of Oyama Sensei's teachings and system. Either way they will teach you correctly. Good luck.