Heres the deal. John and Paul wrote almost all of the Beatle stuff. George became a very accomplished song writer, but not until later. Ringo was and is not a very good song writer. Most of his solo hits were written with help from other people. And, comparing John and Paul is pretty much useless because they both were great and their careers practically mirror each others, but in different manners.
Lets not get into the abilitys of playing the instruments. The Beatles were not the greatest musicians on their respected instruments and there are better players technically. The one point to remember is the song writing aspect. When you see composers like Beethoven, Bach, Shubert,etc,,,,well Lennon/McCartney are spoken with the same breath. To be 1/2 of that combination makes one special. Its not hard.
By the way, I see you must be a pretty big Paul fan with your avatar and your 'Rocky' signature. Please dont try to goad us into a Paul vrs. John thread because its a futile subject.