Neither alone were as good as they were together.
I can't deny that. But if you take a look at their most poplar songs it was Paul's melody and a mix (I think) of Paul and John working together on the lyrics. Paul was philosphically light and John was heavy. So instead of Paul playing with sheep and John being deep and heavy you got a great song with good lyrics.
So instead of Paul playing with sheep and John being deep and heavy you got a great song with good lyrics.One of my favorite examples would be "We Can Work It Out".
A good song made great with John's addition of:
Life is very short, and there's no ti..i..i..i..ime, for fussing and fighting my friend.