Re: Kokikai v. Aikikai
I've trained with dojo that came from a kokikai background, and felt some of their people since Maruyama Sensei came back into the picture from some time off (he was in philly for a long time, but left the city some time ago).
I think the best of their system work on some very interesting "internal" stuff. It seems that after his hiatus, he came back with some very interesting results from solo training during that time. But I don't really know that much...just what I felt from some students of his after a seminar. Very strong, relaxed, and connected. I'd recommend training in the dojo for some classes, see what you think. It seems not all dojo have picked up on his changes, but I can't be sure of that.
As for difference with aikikai, they were ki society for a while before Maruyama moved off on his own.