I read YouTube today, oh boy.....
Actually it was a few days ago and it brought a wry smile to my face as it was a Beatles fansite and this very subject cropped up...unlike this forum, the protagonists there were unfamiliar with this saga; it seemed a fairly new controversy to them. The consensus seemed to be that John initiated and carried the "Aaaahhhh" with Paul joining in about half way through.
Personally I think there is a good case for suspecting they both sang it, but I always felt John had the stronger and more distinctive voice, so it's his "aaaahhhh" which always prevails in my ears.......