The debate over what makes art (be it music, painting, literature,...) great has been going on for a long time. In recent decades, those who argue that it's relative have been winning the debate.
I don’t tend to agree. I side with those who posit that the ultimate test of greatness is whether it lasts. That is, does it speak to more than one generation, in fact many generations.
On that basis, Bach's Brandenburg Concertos, Da Vinci's Mona Lisa, and Shakespeare’s Hamlet pass the test.
So far the Great American Songbook is holding its own. Will the Beatles do as well? Only time will tell.
My concern here is that good music may not get the chance. As long as there are museums and libraries (real or digital), visual and literary art will be viewed and read. I’m just not sure that music will continue to be evaluated on the same basis. I fear that future generations will never have heard of the Beatles, let alone Gershwin or Bach.

Cheers! -Alastair