Actually the mp3 standard is similar to CD at 16bit/48Khz sampling rate capping(44.1 for CD) but when a CD is ripped into an mp3 , the bitrate falls from 1411 kbps to 128 kbps, which does result in loss of quality because some of the information is completely and irreversibly lost. The instruments sound less natural, the overall loudness comes down, the soundstage gets closer, the drums are less deep and the flute is less serene. And it is hugely noticeable. the difference between the sound of CD and mp3 is like the difference between being treated at Taj and being served food at McDonald's. Many people believe that you need a high end system to notice the same but wait. But on any proper system, you can tell the difference.
eventough ,that the fraunhofer algorithm (upon which the mp3 format is based) is highly efficient way of compressing as it takes into account the psychoacoustics and human-perception into account to achieve a high compression to achieve a decent sound. But its up to you to decide whether you want a 'happy-meal' or 'four course meal'
As far as the mp3HD is considered, yes it is CD quality lossless compression but occupies larger space due to 500-900 kbps !