Assuming you're using a 1920x1080 display (LCD, Plasma, or projector) - so the video signal of non-native resolution (e.g. 480 i/p, 1080i) should eventually be converted (up-scaling and/or de-interlacing) to a 1080p signal before it can be fed into the display panel.
In theory, it would be better to make sure the up-scaling / de-interlacing is occurred in the piece of equipment (BDP, AMP, or display) that is the best to do the job. For example, if you have a low-end BDP that you know its video processing chip is not a very good one, but you have the AV AMP that features a very good video processing chipset (e.g. HQV, Marvel, etc.), it would be better to set Auto (or bypass) in the BDP, and set 1080p in the AV AMP output resolution, so that the BDP is forced to output, e.g. 480i / 1080i native disc resolution to AV AMP, and the AV AMP is forced to do the up-scaling / de-interlacing using its good video chipset. If you know the TV or projector is better to do this job, then set bypass in all the down-stream equipment and let the display device to do the job.
By the way, you need to test it by yourself if you want to make sure.
Zappiti Pro 4K HDR Media Player
Pioneer UDP-LX500
Pioneer SC-LX901
JVC DLA-N5
JL Audio E110
PS Audio Power Plant P10