There's much discussion and debate about the two primary "food groups" of tube amps. Personally, I think the online debate is a little silly. It's a little like debating who makes the "best" pickups? Or bolt-on vs set necks. As a rule, I think we guitarists (especially me) tend to obsess over our gear too much. Here are the basic differences...
In a Class A circuit, the current is flowing at all times through the tube. In a Class “A/B” design, a negative “bias” voltage is applied to the grid, which will cause the tube to “shut off” when the audio waveform is below a certain point. Hence the term "push-pull".
There are a few general characteristics that can be attributed to these two architectures. These are general as every amp is different, even different examples of the same model.
We associate the sound of a Class A amp as more "vintage" and "tactile". This is because they are compressing and distorting the signal more. Their current is maximum at all times, so a Class A amp will have a smooth compression. The tradeoff is that they tend to not have a lot of headroom because of their lower plate voltages.
Class A/B amps are thought to have wider dynamics. They sound punchier, tighter, and cleaner than a Class A, making them a good choice for players using pedal-based distortion. Plus, with the same power tubes the Class A/B will produce two-to-three times as much power as their Class A counterpart. And since they are “idling” with lower plate current, you can expect longer tube life.