Imaging flow cytometry (IFC) produces up to 12 different information-rich images of single cells at a throughput of 5000 cells per second. Yet often, cell populations are still studied using manual gating, a technique that has several drawbacks. Firstly, it is hard to reproduce. Secondly, it is subjective and biased. And thirdly, it is time-consuming for large experiments. Therefore, it would be advantageous to replace manual gating with an automated process, which could be based on stain-free measurements originating from the brightfield and darkfield image channels.To realise this potential, advanced data analysis methods are required, in particular, machine learning. Previous works have successfully tested this approach on cell cycle phase classification with both a classical machine learning approach based on manually engineered features, and a deep learning approach. In this work, we compare both approaches extensively on the complex problem of white blood cell classification. Four human whole blood samples were assayed on an ImageStream-X MK II imaging flow cytometer. Two samples were stained for the identification of 8 white blood cell types, while two other sample sets were stained for the identification of resting and active eosinophils. For both datasets, four machine learning classifiers were evaluated on stain-free imagery using stratified 5-fold cross-validation. On the white blood cell dataset the best obtained results were 0.776 and 0.697 balanced accuracy for classical machine learning and deep learning, respectively. On the eosinophil dataset this was 0.866 and 0.867 balanced accuracy. From the experiments we conclude that classifying distinct cell types based on only stain-free images is possible with these techniques. However, both approaches did not always succeed in making reliable cell subtype classifications. Also, depending on the cell type, we find that even though the deep learning approach requires less expert input, it performs on par with a classical approach.