The Lennon-McCartney divide often seems to polarise people; I tend to be of the opinion that they worked much better together than on their respective solo endeavours, though; I feel much the same about Floyd's Waters and Gilmour, too, both of whom seemed comparatively weak as solo songwriters (yeah, waters could do "intense", but without Gilmour's melodies to tame his writing it was a bit too much...)
Don't get me started on Pink Floyd! Another great band. Yes I think Pink Floyd did better stuff when they were together as a band than when they split. It's too bad that Gilmour and Waters can't reconcile because they are both great musicians.
I will stay away from the Lennon-McCartney divide then. I thought some of their fighting seemed petty and a bit childish (writing songs dissing each other), but great artists often are difficult to get along with (especially with another artist).
Freddie Mercury said in an interview that they stayed together for so long (13 years then) because even though they were all strong-minded musicians and were always fighting in a sense, they were basically doing 'solo projects' the whole time they were together as a band and that is what made them more diverse.