Objective quality assessment of digital holograms has proven to be a challenging task. While prediction of perceptual quality of the recorded 3D content from the holographic wavefield is an open problem; perceptual quality assessment from content after rendering, requires a time-consuming rendering step and a multitude of possible viewports. In this research, we use 96 Fourier holograms of the recently released HoloDB database to evaluate the performance of well-known and state-of-the-art image quality metrics on digital holograms. We compare the reference holograms with their distorted versions: (i) before rendering on the real and imaginary parts of the quantized complex-wavefield, (ii) after converting Fourier to Fresnel holograms, (iii) after rendering, on the quantized amplitude of the reconstructed data, and (iv) after subsequently removing speckle noise using a Wiener filter. For every experimental track, the quality metric predictions are compared to the Mean Opinion Scores (MOS) gathered on a 2D screen, light field display and a holographic display. Additionally, a statistical analysis of the results and a discussion on the performance of the metrics are presented. The tests demonstrate that while for each test track a few quality metrics present a highly correlated performance compared to the multiple sets of available MOS, none of them demonstrates a consistently high-performance across all four test-tracks.