Lossy image compression is a popular, simple and effective solution to reduce the amount of data representing digital pictures. In most lossy compression methods, the reduced volume of data in bits is achieved at the expense of introducing visual artifacts in the picture. The perceptual quality impact of such artifacts can be assessed with expensive and time- consuming subjective image quality experiments or through objective image quality metrics. However, the faster and less resource demanding objective quality metrics are not always able to reliably predict the quality as perceived by human observers. In this paper, the performance of 14 objective image quality metrics is benchmarked against a dataset of compressed images labeled with their subjective quality scores. Moreover, the performance of the above objective quality metrics in predicting the subjective quality of images distorted by both conventional and learning-based lossy compression artifacts is assessed and conclusions are drawn.