This article gives a nice overview without being too complicated.
https://headfonics.com/dsd-vs-pcm-real-competitors/
Here are some results from this article that make most sense IMO:
If reconsider some of the common myths or opinions of DSD and PCM we have 3 we would like to focus on:
1. DSD can be considered as format superior in audio quality than PCM.
For DSD noise is pushed to inaudible (high) part of the spectrum. For pushing (noise shaping) significant energy of noise out of the audible range you need a reserve of the band. I.e. higher sample rate, than for PCM, is needed.
PCM quantization noise correlates with useful signals: no signal equals no noise. DSD noise does not depend on signal and is present in silence also. DSD DACs eliminate this noise.
Applying a DSD-DAC allow maximally simplify scheme and adjusting of DAC. DSD DAC is a simple low-frequency filter (that passes low-frequency audio only). It is a higher sample rate than for PCM and simplifies the design of an analog filter. No need for steep transients to the suppression area as you need for PCM. No need for so many precise components.
Almost all modern DAC use internal PCM to DSD conversion for digital-analog conversion. If you use DSD as an end-user format you need 1 precise reference voltage and simple analog filtering only. I.e. same result with less effort than “native” PCM.
I have yet to compare digitizing/restoring to the analog of the square wave for PCM and DSD. There is an advantage in DSD due to its steeper front and less ringing in front/end sides of square impulse. Let consider how to ideally digitize/restore the square wave.
A Square wave has an infinite spectrum. I.e. for ideal digitizing/restoring you need infinite sample rate. DSD has a significantly higher sample rate than that of PCM. It is the reason for a steeper front/end of the square impulse.
Lower ringing for DSD is the result of a shallower filter than that used for PCM signals that have lower sample rates. On the flip side, using wider (more 20…24 kHz) bands for DSD generates more noise energy particularly beyond 24 kHz. I.e. price of a better form of a square wave is a higher noise level.
Lesser ringing due to a shallower DSD DAC filter (less ringing) leads to worse filtration. Thus leading to a higher noise level. By increasing the PCM sample rate it is possible to achieve a steeper front/end of the square impulse also. I.e. no difference between DSD and PCM in the approach to restoring the square wave. There are results of sample rate and filter steepness only.
Digital audio format quality is the degree of loss of an original analog waveform that is restored from digital forms.
1. It is technically impossible to compare DSD and PCM as pure digital formats. You need to compare released systems, that use these formats.