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Neural network-based models augmented with unsupervised pre-trained knowledge have achieved impressive performance on text summarization. However, most existing evaluation methods are limited to an in-domain setting, where summarizers are trained and evaluated on the same dataset. We argue that this approach can narrow our understanding of the generalization ability for different summarization systems. In this paper, we perform an in-depth analysis of characteristics of different datasets and investigate the performance of different summarization models under a cross-dataset setting, in which a summarizer trained on one corpus will be evaluated on a range of out-of-domain corpora. A comprehensive study of 11 representative summarization systems on 5 datasets from different domains reveals the effect of model architectures and generation ways (i.e. abstractive and extractive) on model generalization ability. Further, experimental results shed light on the limitations of existing summarizers. Brief introduction and supplementary code can be found in https://github.com/zide05/CDEvalSumm.