Remote sensing data are widely used in numerous applications. A conventional task solved using remote sensing images is their classification. The classification maps are commonly produced by some pre-trained classifiers applied either to uncompressed or compressed images where lossy compression is often needed and employed in practice due to the necessity to reduce data volume at stages of image transfer and storage. Then, the classification accuracy depends on the characteristics of an image, a classifier, and a coder used. The main subject of this paper is the factors that determine classification accuracy. One of them is compressed image quality. We fix the quality of compressed image quality characterized by the peak signal-to-noise ratio for several coders and rely on the same training approach. Our goal is twofold. First, we would like to consider classification accuracy for two approaches to classifier training: based on undistorted data and images with simulated distortions. Second, our desire is to compare the performance of different techniques of image compression. The task of this paper is to obtain an idea is it worth training the neural network classifier for uncompressed images or images of similar quality to the quality of compressed data to be classified. The coder’s influence on classification results is of special interest as well. The main results are the following. First, the classification accuracy is almost the same for classifiers trained for uncompressed and simulated compressed data for the general distortion model. Second, there is a certain difference in the classification results for different compression techniques studied. Lightly better classification results are observed for data produced by more sophisticated (modern) coders. Experiments have been carried out for two real-life three-channel Sentinel-2 images of Kharkiv and the Kharkiv region having different complexity. Four typical classes have been considered. As a conclusion, it is possible to state that either the general model of distortions must be modified or the classifier training should be performed for data produced by the corresponding compression technique.