The list is utter crap. Hey Jude and Let It Be ahead of Eleanor Rigby, I Am The Walrus or Happiness Is A Warm Gun? The Rolling Stone isnīt worth the paper it is printed on.
I think the only one who gets "sympathy-points" here is McCartney for his life after the breakup, because of his "Gooder" image until this day, how he stood by Linda and what happened with Heather Mills, while Lennon is remembered for his time with Yoko Ono...and everyone hates Yoko Ono.
My vote definitly goes to Lennon. To simplify, John was the artist, Paul was mainstream. Lennonīs "edginess", as you call it, was so influential to what the Beatles represent and stand for until this day, that thereīs just no way around him, imho.