The main difference would be in the amount of buffer needed to store data. In the case of a PCE, that's next to zero, which is fine for a home console, but for a portable, it would last about an hour on batteries, without everything else combined.
For a modern(ish) discman, or minidisc, most of the data is stored in RAM, but with a 1x CD ROM, it's going to constantly have a motor spinning, which is more power than solid state or a new LCD. And LCDs aren't tha bad either, AAIK, it's the backlighting that kills.