Correct me if I'm wrong, but do we not agree that tonearms do affect sound quality, and the point of this thread is how best to assess that? After all, if they do not, then it shall make no difference which one we buy or use.
As for how to check for differences, it seems the best chance would come from two tables of the same make and model, with the same cartridges of similar hours usage, feeding into the same electronics and speakers. The only difference would be the tonearm on each table. Listening performed blinded during the playing of the same LP on each table. Results in terms of preference would be valid for that cartridge only. That would be the science-based approach, and it is unlikely anyone would bother to do it.
The unscientific approach is one that, I think, still has some validity: a long term comparison and you see how much you are tempted to play music, and how long a session lasts. Lots of times I have liked a component, only to find myself choosing to do other things rather than listen to music. This is using the entire neurological path from eardrum to cortex as a meter that measures desire to listen to music. And that result, if it is to be trusted at all, can only be trusted by the owner of the brain concerned!