Their attacks toward each other were serious,taking the fact that half of Obitos body is made of Hashirama cells if he gets hit in that part he will probably live,wile Kakashi on the other hand might die if he is not a clone(ussualy a lightning clone).
If Obito gets hit by a chidori right through his heart then he will hit the dirt,everything else he probably lives.
Still i think Kakashi would not put himself in such a dangerous situation without a reason(talk no jutsu) or without a backup plan regarding his life,so i would have to say Kakashi will probably live.