I think that a lot depends on the individual, the equipment used and the content.
We have two professional sound engineering people as regular group contributors (possibly more), so in one sense, I would defer to their experience and expertise.
I've done some work in the digital video and audio transmission world, so have some appreciation of the technologies used.
One of the objectives of any form of digital audio or video recording or transmission is to squeeze as much as possible into the bandwidth or storage available while producing quality that is fit for the purpose. In order to achieve this, some fairly sophisticated compression techniques are used. This is not to be confused with the compression that AM pop radio stations use(d) so that the listener could hear the dross that they turn out even in a noisy environment or poor signal. The type of compression used in digital audio systems takes into account the behaviour of the listener's ear and brain and uses a psycho-acoustic model. Simply put, this means that information that the ear is not likely to perceive is thrown away and not transmitted. Of itself, this can save a lot of data transmission.
Here are some papers explaining the techniques.
Given enough bandwidth, the results can sound fine. The problem is that the broadcasters, for most of the channels are using lower data rates than are required to produce good audio quality with some types of content. Therein is the rub.
If you like to listen to classical music and to some types of jazz and have a keen ear, you will notice the effects of the compression at the low bit rates often being used, but perhaps not on a small portable set. For other content such as speech, the effects are less noticable or if they are noticable, less objectionable.
In a way it's a shame. DAB, in principle, should be able to offer good quality results and ultimately I suspect will do. However, like DVB-T (digital terrestrial TV), it is hampered by limitations of the current allocated radio spectrum. Even with today's limitations, there are still the benefits of freedom of interference as long as the signal is good (although one can argue that that can be achieved with FM).
However, the motivation for the broadcasters is to pack as much as they can into the available spectrum, first and foremost. For example, a satellite transponder will deliver one analogue TV channel but 6-8 digital channels. The problem is that the content does not in general improve.
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