Bagging (or Bootstrap Aggregating), uses a different random subset of the original dataset for each model in the ensemble. Specifically BigML uses by default a sampling rate of 100% with replacement for each model, this means some of the original instances will be repeated and others left out. Random Decision Forests extend this technique by only considering a random subset of the input fields at each split.
Generally, Random Decision Forests are the most powerful type of ensemble. For datasets with many noisy fields you may need to adjust a Random Decision Forest's "random candidates" parameter for good results. Bagging, however, does not have this parameter and may occasionally give better out-of-the-box performance.