THD stands for Total Harmonic Distortion.
Let's imagine an amplifier is reproducing a 100 Hz bass tone. The amplifier will also produce harmonics of that tone at much lower levels. How high in amplitude these harmonincs are and what type of harmonics will make a difference on how the amplifier sounds.
A solid state amp will produce harmonics from that 100 Hz tone, so 300 Hz, 500 Hz etc. These are called odd order harmonics. A tube amp will produce even order harmonics- 200 Hz, 400 Hz etc. Why this happens, I don't know. Many (including me) find even other harmonics less offensive (or even pleasing) compared to odd order.
The lower the amounts of the harmonics are compared to the desired frequency, the lower the THD.
But lower THD doesn't necessarily mean better sound. Crank up negative feedback in a circuit and THD drops. My experience tells me most amplifiers with low or even no negative feedback sound better.
I'm not surprised that your amp with higher THD sounds good. It's a Pass design and has very low or no negative feedback.
How quiet an amp is is measured in signal to noise ratio. The SNR of vinyl is around 70 dB, a CD is >90 dB. Any quality amp should be around 85 dB and higher. Usually this is where tubes fall short- it's easier to make a quiet solid state amp. In any event, the amp will be quieter than the vinyl itself. Don't get too hung up on this. Sutherland for example does not publish this spec, but anyone who's heard one knows they are quiet as church mice.
Your best test instruments are on the sides of your head. Trust them over a spec sheet.