One possible difference is the nature of the "worlds" that have been created in the two types of fantasy, in the sense that one was created piecemeal by many different writers and authors, and the other is often the version of a single creator.
Take the example of Homer and Virgil mentioned earlier. Homer and Virgil are considered part of Greek myth, but they did not create it on their own. What we know as the world of Greek myth consists of a whole collection of stories and legends, created by different authors at different times, that all coasleced into a larger mythos that we now study today. Greek mythology, and likely the mythology of most other world cultures, did not spring from a single creator; no single person offered an overarching vision and structure to it. Homer certainly made his own original contributions, but he also took a lot from earlier myths, tying his own work into it. Unlike with modern fantasy, when the creator's influence can be clearly seen, Homer's contributions are part of the "foundation", so to speak.
Now, consider modern fantasy. Many of the classic characters and universes, both inside and outside fantasy, of our times are the creations of a single person, who develop the universe and give it an overarching tone and direction. Tolkien developed Middle Earth practically on his own; Robert E. Howard is the sole creator of Conan and Hyboria; H.P. Lovecraft created the Cthulu mythos; George Lucas is supposed to be the original creator of the Star Wars universe; Gene Roddenberry created Star Trek; and so on.
This even extends into D&D and fantasy RPGs: Gary Gygax developed a lot of the 'mythos' that has come to define D&D, with its cosmology of the Planes, the way magic generally tends to work, the various monsters and creatures that exist in the world, and so on. Ed Greenwood established the tone for the Forgotten Realms, and so on down the road.
The criticial difference between these universes and those of ancient times is that the new ones can be clearly traced back to one creator, or a small group of people. His or her first writings will tend to establish a direction for later writers to follow, and conventions that often determine if fans accept or reject new contributions.
Of course, as time goes on and the new universes develop, new writers will come to add their own contributions. Other writers came to add their own contributions to the Cthulu mythos, sometimes with Lovecraft's own encouragement. Stan Lee, Jack Kirby and the rest created the classic Marvel characters, and later writers would develop these aspects of the Marvel Universe and add their own characters, many of whom become key parts of the universe itself. Various aspects of the Star Wars and Star Trek universes have been developed by such things as tie-in novels, fan works, later TV shows, and what have you. Gygax established a lot of the basic mythos of D&D, but later writers would add in their own bits and pieces, and make their own creative contributions.
But the key aspect is that there's generally a tone that's established, especially when the work is quite clearly established by a single creator, as with Lovecraft and Tolkien. Others might make their own additions later on, but it was Lovecraft and Tolkien themselves who established the tone, and what could and could not be done. Fans of the various universes can and do pick up on these things, and this leads them to either accept or reject later developments based on their perceptions of whether it fits with the unvierse or not.
