What do you think are the particular qualities of the music of the "great" composers....?

It may just be the time period these composers were from. They were the inventors of the time period itself maybe. The other composers that weren't one of the "greats" maybe had Beethoven as a teacher or a role model. They followed in their foot steps. Some composers that aren't seen as great probably imitated some of Beethoven's work and then put their own style into it. But the "greats" pulled it from their genius brain and got it from no one else.