Quality of art absolutely exists, but it’s not a linear measure. For instance, it’s pretty straightforward to tell how technically skilled one is with a particular medium, whether it’s with a brush and paint, a guitar, or whatever. Any given piece that is virtually the same but one is done by a technically more skilled person will generally be better, like if two bands cover the same song, generally the more technically skilled band will sound better. However, technical skill is not enough because there’s plenty of examples of terrifically skilled artists turning out terrible pieces. How many well regarded actors haven’t put out a mediocre performance in a dud movie?
Another important dimension is message, as in, how effectively does the artist convey the message? Do lots of people get the same sort of message or is it all over the place? Does it convey the complexities of it or just get a very basic idea across? A painter may have enough technical skill to create a nearly photo-realistic painting, but it’s somehow lifeless; whereas another painter who is clearly less skill is able to express some depth about the subject, whether she’s happy or sad and all these sorts of things.
Composition matters, in that one may have amazing technical skill and even be able to communicate, but it’s just a mess and not really particularly appealing. For instance, one could make a piece that is skillfully drawn and expresses a message well but utterly lacks in basic composition because it’s off-balance, not because that’s part of the message, but because it just wasn’t designed that way, and it comes off very poorly and unappealling. Even pieces that are specifically designed to be chaotic by a good artist will generally show aspects of good composition by deliberately going against certain general rules of composition while maintaining others or making effective use of contrasts or the like. For instance, a poor attempt in music will often be someone playing essentially random notes with no sense of time, even if its played really fast and even though that does indeed express chaos, it’s very unpleasant. A good composer will make use of unusual time-signatures to throw the rhythm off while still maintaining some rhythm, or make use of unusual scales, so it has a different harmony, but still maintains a level of structure, or make use of dynamics or timbre to create contrast.
There’s also effective use of a genre. Where one can be have all of the above but do a terrible job of expressing it within that genre. As an example, trying to do a dance song with bizarre time signatures or controversial lyrics probably won’t be very effective, but it might work well in metal or rock. Obviously, one can define one’s own rules to some extent, and often the very best artists in any medium will be pioneers of a genre, but there’s still some set of rules to whatever genre or sub-genre they’re defining.
There’s others, but I think I’ve given the idea. We can judge any piece relative to any other piece linearly based on a single one of these things, but when we’re trying to put them all together, we’re all going to evaluate them differently and they even weigh in differently based upon their relative strengths. For instance, I generally highly value technical skill, but a few of my favorite songs are actually pretty simplistic, they just really do a great job in conveying the message and have exceptional composition. But I also readily admit that it’s not particularly high quality in terms of technical skill.
Now, there are of course subjective measures too, like a particular genre or particular mediums or whatever, but there’s nothing that makes, say impressionism meaningfully better or worse from cubism or a guitar better or worse than a tuba. The problem is that we all have likes and dislikes and they’re difficult to overcome to appreciate pure quality or lack thereof. I’ll likely rate a mediocre artist of a genre I love to be as good as an above average artist of one I dislike. That’s where the confusion comes in. But at the same time, if I actually focus on specific aspects, I can pull out the quality and make more objective opinions.