Image quality assessment (IQA) is standard practice in the development stage of novel machine learning algorithms that operate on images. The most commonly used IQA measures have been developed and tested for natural images, but not in the medical setting. Reported inconsistencies arising in medical images are not surprising, as they have different properties than natural images. In this study, we test the applicability of common IQA measures for medical image data by comparing their assessment to manually rated chest X-ray (5 experts) and photoacoustic image data (1 expert). Moreover, we include supplementary studies on grayscale natural images and accelerated brain MRI data. The results of all experiments show a similar outcome in line with previous findings for medical imaging: PSNR and SSIM in the default setting are in the lower range of the result list and HaarPSI outperforms the other tested measures in the overall performance. Also among the top performers in our medical experiments are the full reference measures DISTS, FSIM, LPIPS and MS-SSIM. Generally, the results on natural images yield considerably higher correlations, suggesting that the additional employment of tailored IQA measures for medical imaging algorithms is needed.