My understanding is that it is closer to the shift from VHS to DVD, with improvement being somewhat dependent on the DAC used, and the quality of the output unit (speakers, headphones, etc)
Actually, of equal importance to distinguishing the difference is going to be the quality of the media file itself. A lossless audio file is going to really take advantage of better hardware. If a VHS is transferred to a DVD, the quality is still going to be rather poor, which has nothing to do with the medium it's played back on. However, a native transfer to DVD is really going to make a huge difference.
But I'd say this is more akin to DVD to BluRay. Audio quality is already pretty good using Apple's internal DAC and 3.5mm Jack with any given set of headphones, playing even a poor quality MP3. Playing an HQ sound file over an HQ external DAC with an amp matched to the hardware should be pretty impressive by comparison.