Heres the thing, I respect the Beatles contribution to music but I cannot say I am a fan. I find it very hard to enjoy their music, I mean its catchy but there isn't any "substance" to it that resonates with me. People can say that their music defined an era, but I find that hard to digest when during the Beatles' heyday there was the likes of Dylan, The Stones, Hendrix, Cream, Jefferson Airplane, The Doors, The Grateful Dead, Santana, The Byrds, Simon And Garfunkel and The Animals all with enormous followings on both sides of the Atlantic.
Like I said though, I respect their contribution to music and acknowledge their success. Paul McCartney's other projects are of great enjoyment to me from a musical level, particulary with Wings and as himself.
As for Lady Gaga, whilst she is a talented performer, he music only appeals to a particular demographic, nothing she has written (or co-written) has any timeless appeal to it. Although she could very well be regarded as Madonna is within a decade or so, we'll just see how her career pans out.