Class A or Class D solid-state amplifiers (modern designs)

Trying to label the value and quality of sound from an amplifier based on the class of the design is not useful. 

Totally this. Without knowing your system and budget, it's also difficult to make any suggestions. 

Let’s compare and contrast. Which one is technically better?

Here's what you're up against: distortion. Sure, class A does not have crossover distortion. Neither does class D.  The main thing you're dealing with is IMD and harmonic distortion.

Class A amps make both. They are class A to try to minimize that by being in the most linear portion of the operating curve of the output device (whether tube or transistor). But they will make distortion and unless the circuit is designed to be zero feedback there will have to be loop negative feedback to get the distortion into acceptable bounds.

That's where you get into trouble. Back in the 1970s and 80s, the semiconductors needed to actually be able to run the kind of feedback you need didn't exist. We had to wait until the 1990s for that.

If you're thinking that an entire generation of audiophiles grew up with amps that sound bright and harsh you are correct.

The issue is something called Gain Bandwidth Product. You need a lot lot of it! GBP supports the operation of feedback, and to have it support feedback at 10KHz you need more than was possible before sometime in the 1990s. What happens if there isn't enough GBP is the feedback value decreases at higher frequencies- resulting in higher distortion.

This is why the 1KHz harmonic distortion figure tells you little about the amp. What is more important is distortion vs frequency- it should not rise across the audio band, otherwise the amp will have higher distortion at higher frequencies, and this will translate directly into 'harsh and bright' since our ears convert distortion into tonality.

In addition to the semiconductors needed you also need the design. And the will to create it. That took until the 2000s...

As a result, us older audiophiles have been hearing 'harsh and bright' in solid state designs for decades on at this point. That is literally the reason why there are still tube amps around!

If you've been digging deep, you may have realized this isn't a class A vs class AB thing- both classes of operation have can have this issue.

Class D offers a way around this problem.

In a regular amp, if you try to put a lot of feedback in the design you run a risk of the amp being unstable and prone to oscillation unless the feedback loop is very carefully designed, and maybe even then. The reason is there are frequency poles in every amplifier design and they cause phase shift at high frequencies (often outside the audio band). At some frequency the phase shift is so severe that the feedback becomes positive rather than negative- and so the amp oscillates.

In technical/engineering terms this condition is described as 'the phase margin of the amplifier being exceeded'.

In a class D amp you can put a lot of feedback in the design, with the expectation that it will do exactly this. The oscillation is then used as the switching frequency, killing two birds with one stone.

At this point you can have enough GBP that the distortion remains constant at all frequencies, and the distortion normally caused by the application of feedback can also be cleaned up by the simple fact of so much feedback available. You really need to have 35dB or more of feedback to really allow feedback to work right- less than that and it contributes distortion of its own.

This is very difficult to do in a class A or AB amp, although there are a few examples.

That is why some class D designs can easily keep up with class A designs (and FWIW, I've been working with class A amplifier designs for nearly 50 years, if that means anything...).

My experience with SS, tube, and Class D amps over the years is consistent with what @atmasphere said about the nature of the various technologies over time and how that translates into good sound. I started with Class D amps over 10 years ago and it’s Class D all the way at this point for me. Tubes are fun but pretty much over that.

Jeff Rowland was asked a question similar to this a few years ago and basically replied that it's what a designer does with the technology that counts as opposed to one classification being necessarily better than another. 

I am reading this with great interest.  To date, we have not heard a class D amplifier that competes in sound quality.  We are open to hear something that comes close but not yet to our ears.

Happy Listening.