Vision transformers have attracted much attention from computer vision researchers as they are not restricted to the spatial inductive bias of ConvNets. However, although Transformer-based backbones have achieved much progress on ImageNet classification, it is still unclear whether the learned representations are as transferable as or even more transferable than ConvNets' features. To address this point, we systematically investigate the transfer learning ability of ConvNets and vision transformers in 15 single-task and multi-task performance evaluations. Given the strong correlation between the performance of pre-trained models and transfer learning, we include 2 residual ConvNets (i.e., R-101x3 and R-152x4) and 3 Transformer-based visual backbones (i.e., ViT-B, ViT-L and Swin-B), which have close error rates on ImageNet, that indicate similar transfer learning performance on downstream datasets. We observe consistent advantages of Transformer-based backbones on 13 downstream tasks (out of 15), including but not limited to fine-grained classification, scene recognition (classification, segmentation and depth estimation), open-domain classification, face recognition, etc. More specifically, we find that two ViT models heavily rely on whole network fine-tuning to achieve performance gains while Swin Transformer does not have such a requirement. Moreover, vision transformers behave more robustly in multi-task learning, i.e., bringing more improvements when managing mutually beneficial tasks and reducing performance losses when tackling irrelevant tasks. We hope our discoveries can facilitate the exploration and exploitation of vision transformers in the future.