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Single-photon sensitive image sensors have recently gained popularity in passive imaging applications where the goal is to capture photon flux (brightness) values of different scene points in the presence of challenging lighting conditions and scene motion. Recent work has shown that high-speed bursts of single-photon timestamp information captured using a single-photon avalanche diode camera can be used to estimate and correct for scene motion thereby improving signal-to-noise ratio and reducing motion blur artifacts. We perform a comparison of various design choices in the processing pipeline used for noise reduction, motion compensation, and upsampling of single-photon timestamp frames. We consider various pixelwise noise reduction techniques in combination with state-of-the-art deep neural network upscaling algorithms to super-resolve intensity images formed with single-photon timestamp data. We explore the trade space of motion blur and signal noise in various scenes with different motion content. Using real data captured with a hardware prototype, we achieved superresolution reconstruction at frame rates up to 65.8 kHz (native sampling rate of the sensor) and captured videos of fast-moving objects. The best reconstruction is obtained with the motion compensation approach, which achieves a structural similarity (SSIM) of about 0.67 for fast moving rigid objects. We are able to reconstruct subpixel resolution. These results show the relative superiority of our motion compensation compared to other approaches that do not exceed an SSIM of 0.5.