(this answer from limited practical experience 10 years ago, but at least the theory doesn't go out of date):
random forest is less prone to over fitting as each tree in the ensemble is independent, if the base tree doesn't over fit then a random Forest of them also will not over fit. Whereas trees in a boosted model are not independent, boosting trains a sequence of models where model n depends on the previous models.
This is a double edged sword: you can probably get better predictive accuracy with boosting if you have enough data & have controls to prevent over fitting. Whereas a random forest is much more idiot proof to over fitting but it will not perform as well as a boosted model trained but not overfit on a large dataset.