Since our understanding of ancient painting derives primarily from a few literary sources (above all, the 35th book of Pliny the Elder's Natural History) and the frescoes of Pompeii and Herculaneum, we aren't really in a position to evaluate its technical achievements.
That said, the Greeks and Romans certainly recognized a canon of "old masters," of whom the most celebrated was probably Apelles. Pliny the Elder, at least, was a fan:
"Single-handed, he [Apelles] contributed more to painting than all the others together, and even went so far as to publish some treatises on the principles of the art. The great point of artistic merit with him was his singular charm of gracefulness, and this too, though the greatest of painters were his contemporaries."
Apelles was the court painter of Alexander the Great (who made it illegal for any other painter to represent him), and was so favored that the king - or so were told - allowed the artist to marry his favorite concubine. Apelles, it was said, made this concubine his model for his famous painting of Aphrodite rising from the sea.
Unfortunately, no painting of Apelles (or any other Greek master) survives. Many of his masterpieces were brought to Rome, where they were displayed in porticoes and temples. Even in antiquity, however, these had begun to decay. Pliny, for example, describes the fate of Apelles' painting of Aphrodite rising from the sea:
"The lower part of the picture having become damaged, no one could be found to repair it....Time, however, and damp at last effaced the painting, and Nero, in his reign, had it replaced by a copy, painted by the hand of Dorotheus [a contemporary artist]"
We do possess a few impressive examples of fourth-century Greek painting, above all the frescoes in the Tomb of Philip II at Vergina. But the famous Alexander Mosaic from Pompeii (image), thought to be a copy of a painting by a contemporary of Apelles, shows us what treasures we've lost.
Although many wall paintings, some very well-executed, are preserved at Pompeii, Herculaneum, and the villas around (and, occasionally, elsewhere), we know less about the great painters of the Roman tradition. The sort of wall decoration that survives at Pompeii was usually executed by craftsmen working from the ancient equivalent of pattern books; the real prestige pieces created by highly-regarded Roman artists, which have not survived, may have been qualitatively different.
Not all Mosaics are cartoonish and flat. There was a time with very realistic mozaics. Many however were copied to simulacrum and over time they got less detailed.
https://en.wikipedia.org/wiki/Alexander_Mosaic
This is a pretty famous mozaic. However, this famous one is most likely a copy. In one of my art history classes we discussed this in detail.
What tends to happen in art is Art starts off basic, it develops into a very highly detailed craft, and either artist abandon high detail in favor of stylization, or over time it just gets bad. Take the game Zelda: The Wind Waker for instance. Games were developing towards more realistic technical projects, and Nintendo decided to take a step away from that and create a stylish cartoon game. It wasn't because the artist weren't capable, they just wanted to do something different. It could be that the artist preferred a specific style to some uncanny valley. It is also worth noting that many sculptures that we see were painted at some point. Reproductions of these are simply copies of the art in the current form, and are rarely ever painted.
Another thing to consider with art archeology is we only have what we've found. Not all materials can stand the test of a few thousand years. It's very likely that some very nice work has been lost over time. Even things in the 20th century are most likely lost forever. It is unlikely anyone will ever see the movie London After Midnight again as it was lost in the 1965 vault fire. The 1925 movie Wanderers of the Wasteland decomposed into jelly. It is very likely the majority of murals decomposed into dust, or at least the paint flaked off. Many temple have pretty intricate friezes. These friezes were often carved in a way that lasts the test of time. One of the reasons many ancient Stelae still survive is they were carved into very durable materials. Paintings are by form not durable as they fight against gravity.
So my previous comment was flagged for not conforming to the standards, and I am procrastinating from Grad school commitments, so here goes. Again, a little bit of background. I am an Art conservator, specialising in early photography; but previously worked a lot on paintings, both on walls and paper, in India. So, my info will be biased towards that.
A major problem with looking at “art”, both two, and three dimensional, is that we look at it from the visual culture we have been acculturated in, so the things we tend to look at works from other cultures and other periods from the lens of our own visual culture. Thus, when we look at Greco-Roman arts, we are struck first with the muscular realism of their sculpture, and then, for the lack of a better term, jankiness, of the painted works; for example, compare https://en.wikipedia.org/wiki/Laoco%C3%B6n_and_His_Sons#/media/File:Laocoon_and_His_Sons.jpg with https://www.metmuseum.org/toah/works-of-art/03.14.4/
Now, a major concern with art history is the question of influences. A fair amount of it is teleological, where art historians try to draw a line from the past to future, to explain how the visual arts developed. A trite example, again in the greco roman vien would be the difference in the rendering from the archaic period, again to the sculture of Laocoon https://en.wikipedia.org/wiki/Ancient_Greek_sculpture#/media/File:Ac.kleobisandbiton.jpg
While this can be a valuable approach to contextualise the visual arts, it gets hard in case of ancient art, as u/toldinstone said, where we only have textual descriptions to go on. In that case, we refer to written accounts. Historians everywhere will sigh, because as they know, textual evidence has to be taken with a grain of salt. Herodotus with his ants protecting gold in india, I am looking at you. Anyway, this dependance on textual evidence led to a large scale study of materiel history, in a means to validate what was learned through text, which is the field of technical art history. Here, we generally use technical analysis, such as microchemical testing, XRF, XRD, SEM, and a whole slew of chemical and physical analytical techniques to figure out what makes up art, and then validate by reconstructions.
This brings us to the supplementary question, which I will try to answer first. It is a commonly accepted fact that the materials affect the final product in the arts. The development of oil paints, whose first well known proponent was Van Eyck, led to developments in rendering that were simply not possible before that period, because the materials did not allow for it. Compare the Ghent Altarpiece with the Tarlati Polyptych here
https://en.wikipedia.org/wiki/Ghent_Altarpiece#/media/File:Lamgods_open.jpg
While there was a temporal and geographic difference in the paintings, a major difference too was the materiel, which was tempera in the case of the Tarlati polyptych, and oils in the Ghent Altarpiece. It is just a physical reality that paintings in oils will be richer and more saturated, because drying oils can hold more pigment in comparison to eggs, from which tempera paints are normally made.
Moving from that assumption, then we can say that the technical studies of the greco-roman paintings would tell us a lot about the materials used, and they do. We know to a fair degree about what pigments were used, because we had a fair idea about how wall paintings worked in the mediterranean era. We knew that they used lime as the binder, and thus had to use pigments that would not alter as the lime cured, because that stuff is pretty alkaline. We knew that the painters worked in giornate, or daily sections, because lime only stays good for so long when exposed to air. In a manner it became effectively dogma, because the specialists in the 60’s Mora, Mora, and Phillipot did a lot of work,and wrote the de facto textbook on conservation of wall paintings, called “Conservation of Wall Paintings”. It helped that Phillipot was a major writer on art historical matters, and spearheaded the education of pretty much an entire generation and a half of conservators. https://heritagesciencejournal.springeropen.com/articles/10.1186/s40494-016-0111-4?fbclid=IwAR3boAx5EHXBccjHnmXSblCz6nx2yv5UD8XC1ktrOT5tH8g2619lDYcGYLk
This paper goes into this topic in detail.
Continued in comments because of posting limits
