If PSX had an MPEG decoder in hardware, it would play VCDs out of the box. Instead, playing VCDs/MPEG video requires a silly third-party hardware add-on:
Aside from the choice of codec, the main thing that affects video quality is the amount of compression. More compression makes for a grainier video with more artifacts. On PSX, they would tend to save space by eliminating frames, which is why PSX videos sometimes suffer from low framerates. Lowering resolution to save space was done on both systems.