I do't know if I have some kind of bias on this, but while researching Chinese myths and legends I found stories that seemed surprisingly modern, for example there are stories of people going to law school, like the Butterfly Lovers, or the happy ending is the main couple opening a Pharmacy together.
One story (I can't find it's name right now) begins with a dude dropping out of law school and ends up becoming a sort of "Zen saint" or some kind of deity in the Zen religion.
This is very weird to me because you never hear of Sigurd nor King Arthur dealing with doctors or lawyers, much less those people being the main characters in those legends.
And in general chinese myths and legend seem to focus more on "regular people", or rather, their stories seem to be about regular people that became exceptional, instead of being about people that begin being exceptional or destined to be so.
Why is this?, what influenced both of this cultures to have mythical traditions that differ so much in this particular aspect?
In very broad terms, Chinese society had a much longer and less interrupted tradition of literacy, legalism, and institutionalized medicine/pharmacology. The retreat of the Roman empire saw the reduction or disappearance in Europe of many similar formal institutions. And generally the European elite of the medieval and early-modern period was a martial elite, whereas China had a greater proportion of non-martial bureaucratic elite; so the audience of people for written works was a bit different.
But it is important to look at what time period the myths or folktales you are looking at come from, who the intended audience is, and also consider how you are differentiating myths/legends from more general literary works.
Chaucer's Canterbury Tales (1387) features doctors, lawyers, and characters from a wide range of social backgrounds. Though the Canterbury tales are a literary work rather than a collection of longstanding myths or legends, it does predate the publication of the Mort D'Arthur, which most modern versions of the King Arthur stories are based upon.
The idea that Chinese myths focus more on "regular people", you are conflating thousands of years of extremely diverse western Mythos here. The 'ancient greek and roman myths" that modern readers consume also represent a very narrow band of ancient writings, I think the differences you see have more to do with what you are reading than with real differences between the Chinese and western canon.