Which classifier performs better when using 'class_weight'?
Very good question! I think the plain answer is: no. To my experience this usually depends on the data. Even different boosting methods/tools will perform differently. It often depends on try and error. 

What can make a difference is using L1/L2 regularization, since it can shrink features which are „not useful“ to make a good prediction. 

I cannot think of a theoretical reason here. I‘m curious if someone comes up with a more theory based answer!