12at7 (dual trioded) tubes in general are not a very linear device... (compared to say 12au7's or 12ax7's)(there NOT interchangeable though)
Many times the engineer uses a choice of tube that intentionally to generate mild orders of 2nd order distortion, this delibertly sweeten the sound.
Making a very rich pleasing appeal.
I would consider this a form of processing.
Actually it seems to have a popular following even though it deviates from "a straight wire with gain".
Many power amplifiers especially in "front end gain stages"(preamps) produce this type of effect or distortion.
Otherwise the combination of tubes and circuit criteria selected in the original design choose inherently a more linear plate transfer charastics to produce or attempt to produce a more accurate and neuteral sound.
Especially with open gain (no negitive feedback)
This is a over simplification of course.
The jj brand might be a little better or not. But its not my choise for a audio amplifier. Many times it the amount of gain choise by the designer (a gain of 70 I think), the 12ax7 has a gain of 100 as I remember and the 12au7 has a gain of 20 I think. Then theres other type of dual triodes like the 6dj7 or 6922 which can be set up to do a good job. And then octal base tubes like my old stand by the 6sn7 and the 6sl7 both very good and many o.e.m brands at low and different levels of distortion.
My choice from experence (most the time) for lowest distortion is Electro Harmonic brand.
I personally now individuals that do like them because the DON'T produce enough "sweetness" even in output tubes.
So it one of thoughs things, a dryer sound or richness in the final outcome... your choice.
