who do not consider him the equal of Vergil
I'm a huge fan of Ovid, so forgive me for rambling a bit or going more into specifics than you probably need. Ovid rarely reaches the poetic/emotional heights of Vergil, but faulting him for that would be criticizing him for something he's not trying to do (as he shows pretty clearly when he summarizes the
Aeneid in books 13-14 of the
Metamorphoses and spends as more lines on a digression about an island where people were turned into monkeys than he does on the whole Dido story). Firstly, nobody even comes close to him in how naturally he fits his words to the meter. Dactylic hexameter and pentameter are not natural meters for Latin; they are imported from Greek, and even in Greek they only work because of a bunch of alternate forms unique to poetry. But you'd never be able to guess that from Ovid's use of the meter; more than any other poet, he makes writing in hexameter look trivial. It's hard to describe exactly what I mean by the smoothness of his verse, but later poets (e.g. Statius, Valerius Flaccus) clearly have to try very hard to express what they want to express, and rely on contorted word orders and heavily allusive language, whereas in Ovid it consistently seems effortless, which is super impressive to me. Additionally, he is very unwilling to take himself seriously and everything has at least a tinge of irony behind it. Even his most serious work, the
Metamorphoses, has a lot of self-aware humor, some rather subtle in ways that play with the audience's knowledge of myth and epic conventions.
One of my favorite examples is in the Byblis story (9.450-665, where Byblis falls in love with her brother Caunus and is rejected). There are a lot of amusing and charming details (e.g. her love letter is so long that she runs out of space on the paper; when she is rejected for the first time, she manages to convince herself that the messenger just did a bad job reading the letter). But Ovid also makes fun of the way characters in epic poetry are always able to cite other mythological examples to support their cause: in a soliloquy, Byblis remarks "
At non Aeolidae thalamos timuere sororum! / unde sed hos novi? cur haec exempla paravi?" ("But the sons of Aeolus did not fear the bridal-chambers of their sisters! But where did I learn about these people? How did I prepare these examples?"). What makes this most remarkable is that she's alluding to a description of Aeolus's sons in the
Odyssey (where his 6 sons are married to his 6 daughters) that actually contradicts most of the
Metamorphoses; in other stories within the poem, sons of Aeolus have completely non-incestual relationships. So Byblis literally reaches out of the world of the poem she's in to pull a reference from another poem, then comments on the weirdness of having done that.
A similarly subtle example of that sort of learned humor comes in the argument between Ajax and Odysseus over who deserves Odysseus's armor. Odysseus lists some of the people he killed in the
Iliad, saying "
cum multo sanguine fudi / Coeranon Iphitiden et Alastoraque Chromiumque / Alcandrumque Haliumque Noemonaque Prytaninque" ("with much blood I cast down Coeranus son of Iphtitus and both Alastor and Chromius, and Alcandrus and Halius and Noemon and Prytanis"). This seems like just a boring list of names, but
Alcandrumque Haliumque Noemonaque Prytaninque is a line that's been used in two previous epic poems. It is a direct transliteration of a line from Homer's
Iliad as Odysseus is slaughtering those people (
Alkandron th' Halion te Noēmona te Prytanin te), but the same line also appears in Vergil's
Aeneid in a completely different context. Vergil seems to have just included the line as a little "easter egg" (like "haha, I can fit this Greek line perfectly into Latin, isn't that funny"), and Ovid is one-upping him by essentially saying "Hey Vergil, I caught your little 'easter egg',
and I know my Homer well enough to remember the exact context of the line and put it back in that context."
He also makes fun of the epic convention of adding useless phrases to fill out the meter of a line, and takes that to an extreme by interrupting bits of dialogue with completely useless parentheticals: "
'hi te ad bella pares annis animisque sequentur, / cum primum qui te feliciter attulit eurus' / (eurus enim attulerat) 'fuerit mutatus in austrum.'" ("[Aeacus said to Cephalus:] 'These people will follow you to war, equal in years and courage, as soon as the East wind that brought you here with good fortune' (for it was the East wind that had brought them there) 'turns into a South wind.'")
In general, the work is super charming and fun to read, and there are a ton of memorable scenes for various reasons (Cyclops Polyphemus's love song for Galatea in Book 13 is deliberately written as a parody of terrible love poetry by a hapless brute who's trying to turn himself into a poet, beginning with more than 25 similes in a row that are all based on the pastoral imagery Polyphemus would be familiar with, e.g. "softer than cheese"; Medea's monologue as she struggles to process her love for Jason at the start of Book 7 brilliantly represents her mental turmoil).
I think Quintilian accurately describes Ovid as
nimium amator ingenii sui (over-fond of his own genius), but unlike some later poets that doesn't mar his style. He certainly knows that he's clever and learned and doesn't hesitate to flaunt that, but almost never at the cost of readability or entertainment value. I will say that there's a ton of stuff in the
Metamorphoses, and my perspective is only one approach to the work; the details I've focused on here are not the most famous things about Ovid or the things that have been most influential in the Renaissance/modern canon, and plenty of readers would find themselves struck by completely different things. My guess as to why his influence on the Western canon has been so great is just that he preserves such a large variety of stories rather than going into detail on one story, which naturally affords more material for other artists or writers, and due to the poor preservation of Hellenistic poetry, his account is the best-preserved for most of the stories he narrates.