I assume your question is directed primarily to SS amps, maybe including hybrids.
As also indicated by Stanwal, IMO the answer is; it depends on the amp.
There are excellent sounding Class AB amps and crappy sounding Class A amps. There are so many other factors involved such as the design, quality and size of the power supply; mosfet or bipolar output devices; the number, quality, and matching of the output devices; the use of negative feedback (although some respected designers use local negative feedback); input and output impedance as related to partnering equipment and speakers; power and ability to double down; and other critical design factors. As an example, the Belles 350A Reference amp is said to be a very good sounding amp by virtually every professional reviewer and most owners/listeners who have posted here - and that amp runs in Class B!
Class A amplification is not for everyone, no matter how good they sound. Class A amps are typically heavy, run very hot, use more energy, should not be left powered up all the time (as you can with cooler running Class AB amps) due to wear on internal parts from heat, and are generally more expensive to purchase per watt of power.
OTOH, if you have the ability to buy (and lift :>) quality Class A amplification, and you can deal with the issues listed above, there are some very good choices that many consider to be among the best in SS amplification. In my own experience with Class A, I have owned the Lamm M1.1 hybrids and two different Clayton models, each of which sounded very good to excellent. However, I need lots of power to achieve the level of dynamics I want from my speakers so the Lamm amps (at 100 wpc) would run out of gas at a certain level (although they sounded very good up to that point). My current Clayton M300 monoblocks with the most recent power supply upgrade are the best sounding amps I have owned. They do not run out of gas and offer 300wpc @ 8ohms and 600wpc @ 4ohms, all fully in Class A (when they are switched to high bias). They have a convenient high/low bias switch that can be set to low (200 wpc in Class A) for casual listening and still sound very good. Other Class A amps reported to sound very good to excellent include the Pass XA.5 series of amps (30 to 200 wpc in Class A), Boulders top amps, Lamm M1.2 Reference and 2.2, Krell class A amps, and more I have not listed. At the lower/mid price ranges, many have reported the Monarchy Class A amps to sound quite good, and Clayton also offers some amps in that range.
If I were to generalize based on my experience, in an attempt to answer your question, I would say well designed Class A amps, when compared to well designed AB amps, offer sweeter sounding high frequencies with less tendency towards grain or harshness, seductive midranges that are generally full and rich sounding with excellent harmonics, as well as being more dimensional (although tubes and hybrids do dimensional the best IME), extended decays, full, meaty bass, and a warmth and/or organic nature that adds a level of realism to the listening experience. The better/best Class AB amps can provide these things also, to varying degrees, and tend to sound different, with sharper leading edges (not necessarily in a bad way), more detail at the frequency extremes, better bass dynamics, and perhaps a touch of dryness in the midrange (in comparison). Of course there are exceptions.
As also indicated by Stanwal, IMO the answer is; it depends on the amp.
There are excellent sounding Class AB amps and crappy sounding Class A amps. There are so many other factors involved such as the design, quality and size of the power supply; mosfet or bipolar output devices; the number, quality, and matching of the output devices; the use of negative feedback (although some respected designers use local negative feedback); input and output impedance as related to partnering equipment and speakers; power and ability to double down; and other critical design factors. As an example, the Belles 350A Reference amp is said to be a very good sounding amp by virtually every professional reviewer and most owners/listeners who have posted here - and that amp runs in Class B!
Class A amplification is not for everyone, no matter how good they sound. Class A amps are typically heavy, run very hot, use more energy, should not be left powered up all the time (as you can with cooler running Class AB amps) due to wear on internal parts from heat, and are generally more expensive to purchase per watt of power.
OTOH, if you have the ability to buy (and lift :>) quality Class A amplification, and you can deal with the issues listed above, there are some very good choices that many consider to be among the best in SS amplification. In my own experience with Class A, I have owned the Lamm M1.1 hybrids and two different Clayton models, each of which sounded very good to excellent. However, I need lots of power to achieve the level of dynamics I want from my speakers so the Lamm amps (at 100 wpc) would run out of gas at a certain level (although they sounded very good up to that point). My current Clayton M300 monoblocks with the most recent power supply upgrade are the best sounding amps I have owned. They do not run out of gas and offer 300wpc @ 8ohms and 600wpc @ 4ohms, all fully in Class A (when they are switched to high bias). They have a convenient high/low bias switch that can be set to low (200 wpc in Class A) for casual listening and still sound very good. Other Class A amps reported to sound very good to excellent include the Pass XA.5 series of amps (30 to 200 wpc in Class A), Boulders top amps, Lamm M1.2 Reference and 2.2, Krell class A amps, and more I have not listed. At the lower/mid price ranges, many have reported the Monarchy Class A amps to sound quite good, and Clayton also offers some amps in that range.
If I were to generalize based on my experience, in an attempt to answer your question, I would say well designed Class A amps, when compared to well designed AB amps, offer sweeter sounding high frequencies with less tendency towards grain or harshness, seductive midranges that are generally full and rich sounding with excellent harmonics, as well as being more dimensional (although tubes and hybrids do dimensional the best IME), extended decays, full, meaty bass, and a warmth and/or organic nature that adds a level of realism to the listening experience. The better/best Class AB amps can provide these things also, to varying degrees, and tend to sound different, with sharper leading edges (not necessarily in a bad way), more detail at the frequency extremes, better bass dynamics, and perhaps a touch of dryness in the midrange (in comparison). Of course there are exceptions.