Yes power amp compression in valve amps sometimes allied to power supply sag in earlier valve rectified models. It leads to a more pleasing sort of distortion (compression is distortion). With solid state amps (most Class A/B, G,H and D) the amps keep getting louder until the start clipping which tends to sound harsher than from a valve amp. Some A/B amps use MOSFET outputs that distort/compress more like a valve amp, think Ashdown ABM and Trace Elliot SM. I suspect Handbox also use this topology.