Class A amps (almost) always measure better,
Also not true. AB can have vanishingly low distortion. Compare for instance Pass' class A designs. He deliberately designs for euphonic distortion. He does not make absolutely low distortion amps nor does he wish to. It's exactly his house sound.
So, neither sound nor measurements are better universally by class. Class D for instance can best many Class A for distortion and low output impedance. Not always though.
What is true is that the crossover distortion vanishes with Class A. Sound quality, output impedance, distortion, all vary greatly and overlap with other class of amps.