Both are guite good, but karin is better in my opinion cause it heals much better and has better control

what bug?

I agree with your case.

They only better use for Tsunade will be if your p2&p3 support her not to be controlled or you are very unbalanced. Then if your p1 clears the field from control you can resurrect your p2&p3 but this starts to sound more situational. So overall Tsunade is more situational then Karin. Also Karin may be used in p1&p2 with good success and in end-game when you will need more balance she will be more viable.