128kbps is regarded as the bitrate for optimum performance I guess based on a compromise between audio quality and battery lifespan, it really does depend on the recommendations by the maker of your player.
I had a portable CD based mp3 player, which advised using mp3 at 128kbps, and it did seem to drain the batteries a little bit quicker when using higher bitrates, I guess it's down to how much data can be cached in the processor which determines the time until it needs to retrieve more data, if the bit rate is bigger then the playing time before it needs to get more data will be less that if the bit rate is smaller. With a CD based player you will have a CD player mechanism using power, it will need to spin up to speed, find the data and then read the data before it can stop the CD mechanism, this will contribute significantly to a reduced battery lifespan, and the more the cd mechanism is activated the sooner the batteries will drain.