The systematic monitoring of the Earth using optical satellites is limited by the presence of clouds. Accurately detecting these clouds is necessary to exploit satellite image archives in remote sensing applications. Despite many developments, cloud detection remains an unsolved problem with room for improvement, especially over bright surfaces and thin clouds. Recently, advances in cloud masking using deep learning have shown significant boosts in cloud detection accuracy. However, these works are validated in heterogeneous manners, and the comparison with operational threshold-based schemes is not consistent among many of them. In this work, we systematically compare deep learning models trained on Landsat-8 images on different Landsat-8 and Sentinel-2 publicly available datasets. Overall, we show that deep learning models exhibit a high detection accuracy when trained and tested on independent images from the same Landsat-8 dataset (intra-dataset validation), outperforming operational algorithms. However, the performance of deep learning models is similar to operational threshold-based ones when they are tested on different datasets of Landsat-8 images (inter-dataset validation) or datasets from a different sensor with similar radiometric characteristics such as Sentinel-2 (cross-sensor validation). The results suggest that (i) the development of cloud detection methods for new satellites can be based on deep learning models trained on data from similar sensors and (ii) there is a strong dependence of deep learning models on the dataset used for training and testing, which highlights the necessity of standardized datasets and procedures for benchmarking cloud detection models in the future.