Certainly the mp3 format removes a lot of data from an otherwise complete recording. Mind you, for use on an ipod it doesn't really matter too much.
All my CD's are backed up on lossless codecs which while signficantly bigger file sizes than there mp3 counterparts, at least retain their full audio glory!
Not sure on DAB. There must be a fair amount of data that can be transmitted? Certainly the radio that i pick up on freesat is good enough quality for the speakers and (PC based) amplifier i use.