Ultimately, the creative difference between John Lennon and Paul McCartney can be grasped from a metaphysical point of view. If you do this, it is easy to finally see why John is better, or at least, why he's the better artist. At the same though, it shows why Paul is the more unusual artist.
Put schematically, it's this: Paul sings about what is, John sings about what is not. That's it. Paul loves the world for what it is, he doesn't think of change, of revolution or transformation, but of using his creative power to cast a sacred light on the way things are. John is a nihilist, a negator, but not solely, because his negating energy is driven towards in turn towards manifesting art's utopic possibilities. As an artist, John is driven towards what could be, what might be, what is possible, not what is real - imagine. In a way, however, this is what makes Paul more of an artistic anomaly, because like John he's a genius, but a conservative one - somehow his creative energy isn't tied to nothing, nihilo, non-Being, the way that many artists, including John, are. This is the great mystery of Paul: how can one be so brillantly jacked into creative forces, but in a way that is so rudely de-coupled from all other engagements with non-Being, that is, not with the way things are, but the way they could be?
Think about it, "Revolution" vs. "Let It Be." What could be more antithetical to revolution than saying "just let it be?" Which are also, mind you, "words of wisdom." Why are they words of wisdom? Because wisdom comes from tradition, and tradition always wants you to let it be, not to stir up trouble, not to try and change things.
The metaphysical split between John and Paul is most tactile in the single the Beatles issued right before Sgt. Pepper. It's a John/Paul split, John sings "Strawberry Fields Forever" and Paul sings "Penny Lane." It's all right there. They're both highly nostalgic songs, and both fictionally so, that is, both hearken back to something that doesn't exist. Except that Strawberry Fields never can, which is why, paradoxically, they must be 'forever.' Because what should be proclaimed to be forever, other than something which can never be at all? John sings, famously, that at Strawberry Fields "nothing is real." He also notes "it's getting hard to be someone" and "no one I think is in my tree." Such alienation is anathema to Paul, who's always at home in a crowd, who always seems bloody well at home everywhere he goes. Strawberry Fields is a pretty lonely place. There's no one there, just you and John. "Penny Lane" in contrast is a bustling scene of quotidian beauty, small-town romanticism.
Here's promo videos for both songs. You figure it out.