In the last few years, classification of cells by machine learning has become frequently used in biology. However, most of the approaches are based on morphometric (MO) features, which are not quantitative in terms of cell mass. This may result in poor classification accuracy. Here, we study the potential contribution of coherence-controlled holographic microscopy enabling quantitative phase imaging for the classification of cell morphologies. We compare our approach with the commonly used method based on MO features. We tested both classification approaches in an experiment with nutritionally deprived cancer tissue cells, while employing several supervised machine learning algorithms. Most of the classifiers provided higher performance when quantitative phase features were employed. Based on the results, it can be concluded that the quantitative phase features played an important role in improving the performance of the classification. The methodology could be valuable help in refining the monitoring of live cells in an automated fashion. We believe that coherence-controlled holographic microscopy, as a tool for quantitative phase imaging, offers all preconditions for the accurate automated analysis of live cell behavior while enabling noninvasive label-free imaging with sufficient contrast and high-spatiotemporal phase sensitivity.