Bee will win. Kakashi's Sharigan Prediction won't really help him against Bee's Kenjutsu. Kakashi's raiton attacks will pretty much be useless against Killer Bee. Also there is no suiton source so i don't really see him defending himself properly. Bee is much faster and stronger than Kakashi, he would simply overwhelm him. His doton's may be able to slow Bee down, but i don't see Kakashi killing him. Kakashi lacks the fire power to win. IMO
The only way he could win is by using MS, but i don't think that will come into play in this fight.