They come out the same for me - but the HDRI is missing, as are several V-Ray plugins, so not sure if that has a bearing.
I tried 8 bit and 16 bit PSDs, both Backgrounds looked the same, and that is the same as seen in the PV, and the same as the 8 bit JPG. 16 bit definitely recommended for layers though, since some of those will need the wider bit depth to be stored properly. And be sure you are not mixing layers, as noted the mixing mode may need adjustment. You are comparing just the Background layer? Can you share what you get from this particular C4D file? Could be something to do with Photoshop color management, all else being equal.