I've got a bit more background in machine learning than statistics. Let's say that I want to analyze causal effects based on propensity scores of the treatment and control group. I know that most often the propensity scores are determined using logistic regression. Can I use another algorithm to better handle this estimation for data I know are not linear, like random forests, boosting or neural nets ?

If I do use a different classifier, how can I measure if they're doing better than logistic regression ? Measuring accuracy doesn't really work.