Paul McCartney or John Lennon: who was better?

I have always thought Paul was a much better songwriter, but when I shared this opinion with other musicians I have been met with much resistance. 

I think McCartney seems to have more control over his instrument and is technically a better musician than John, however, John was always the cool one of the two and tended to write more groundbreaking or progressive songs.  Paul also wrote music that was sweeter and more structurally complex in nature with more chords and sections, while John's songs usually were darker, simpler in structure, and might have more improvisation.

Opinions? Questions? Can anyone confirm this or deny this analysis?

TJ of Doppler
www.dopplerband.com
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"I know when I started I would have been happy to sound like the Beatles or Joe Tex or whoever. You want to sound like most bands, you want to sound like their records and that's how you learn your chops."
 
- Jon Anderson of Yes

Hmmm...... As songwriters, they are equals. Paul may have given us "Hey Jude", but John gave us "Across the Universe". Paul may have given us "Blackbird", but John gave us "Julia".  Paul may have also given us "My Love", but John also gave us "Imagine". However, I would say the edge in musicianship goes to McCartney. Now John was no slouch musician, and he could play some mean guitar and was a great vocalist and pianist, but Paul is a true musician's musician. He has great command of all the instruments he has ever played, which includes the drums. Furthermore, Paul is one of the great vocalists of all-time. I was listening to Venus and Mars the other day ,and I still get chills when I hear his vox on "Call Me Back Again".