ear buds

It's true that for a given signal voltage, a 32 ohm speaker will draw less current than a 16 ohm speaker, and you should get slightly longer battery life.

But the loudness of a speaker is determined not only by how much power it consumes, but its efficiency -- how effectively it converts that power into sound. And its efficiency has nothing to do with its impedance.

Either way the audio is a miniscule part of the total current draw of one of these players. The battery lifetime difference between full rated power and muted is perhaps a few minutes.

What about in full size receivers and amplifiers, from say the 60's to 80's. I got the impression somewhere that in those devices the output stage used more than all the prior stages combined, right?

Does accessing memory in an MP3 player etc. take much current?

That's true of pretty much all stereo receivers, but we're not talking about stereo receivers, we're talking about a portable device capable of outputting a few milliwatts to a pair of earbuds, not a few tens to to a few hundred watts to big speakers.

The biggest user of power is the hard drive and display on players so equipped.

Thanks again.