Well in comparison, Kai for sure, has more resemblance to a yak then of a bull. And alot of people agree that Kai is yak. In fact, I do believe some of the officially licensed KFP books also say Kai is a Yak. But the reason the wiki page that Kai is a bull is because that is directly what the Director, Jennifer Yuh Nelson had said. Although it is a possibility that she just made a mistake, who knows.
And for the face off between Kai and Oogway. To me, it seemed Oogway knew he needed to pass on his duties to his successor, at some point. So he just did it at the time he thought was best. So my guess is that he surrendered to Kai, so Po could fufill his destiny as Dragon warrior :) its a matter opinion I guess