I too, cannot see the massive adulation pour on While My Guitar Gently Weeps. ... I hope it's being voted for on merit, and not just because it's George.
I can see plenty of merit in the song, BM, largely because of the different versions I've heard. When the song holds up in different incarnations, it's got to be the song, not just the performance.
To me a strength of the piece is the eerie sense of alienation George achieves with the lyrics-- the singer is in the room, but not part of the group. He's watching the action, being affected by it, but simply observant, not reacting. It's a weird sense of dissociation, which absolutely fits the mood and melody.
In my opinion, which others might not share, I like the incarnations of the song in this order:
#1. Anthology 3-- just George. The intimacy of this take chills and moves me.
#2. Concert for George-- the whole band cooking on this thing, with Paul recreating and exceeding his driving piano intro, and Eric doing the same on his solo-- and of course we have 4 drummers hammering away by this time. Just an awesome production.
#3. Love-- George plus string accompaniment. I don't think it's Sir George's best score, a little too intrusive for my tastes, but it does support the original intimate mood.
#4. White Album--The Beatles. This version sounds the draggiest and tinniest to me. I just don't feel the band was giving their all on this-- but that's the way I feel about TWA and LIB in general. Just not a great period for the band, compared to what they could do when they truly supported each other.