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Pretraining has become a standard technique in computer vision and natural language processing, which usually helps to improve performance substantially. Previously, the most dominant pretraining method is transfer learning (TL), which uses labeled data to learn a good representation network. Recently, a new pretraining approach -- self-supervised learning (SSL) -- has demonstrated promising results on a wide range of applications. SSL does not require annotated labels. It is purely conducted on input data by solving auxiliary tasks defined on the input data examples. The current reported results show that in certain applications, SSL outperforms TL and the other way around in other applications. There has not been a clear understanding on what properties of data and tasks render one approach outperforms the other. Without an informed guideline, ML researchers have to try both methods to find out which one is better empirically. It is usually time-consuming to do so. In this work, we aim to address this problem. We perform a comprehensive comparative study between SSL and TL regarding which one works better under different properties of data and tasks, including domain difference between source and target tasks, the amount of pretraining data, class imbalance in source data, and usage of target data for additional pretraining, etc. The insights distilled from our comparative studies can help ML researchers decide which method to use based on the properties of their applications.