OK, now we're getting into some seeeerious contests here.
I consider both these songs to be major artistic breakthroughs by both bands.
Contest #7: Battle of the 1965 Big Artistic Breakthroughs - "Let Him Run Wild" vs "We Can Work It Out"
Listening to both of these, I can't help but wonder if June-October 1965 may have been the pinnacle of human civilization.
"Let Him Run Wild" - recorded March & June 1965
(if you've never heard this song before, I recommend turning up the volume as loud as you can stand, it's got much better impact that way)
"We Can Work It Out" - recorded October 1965
Where to start? Both songs were preludes to music both bands would begin writing shortly - Pet Sounds in the case of "Let Him Run Wild," and Rubber Soul (or even Revolver) in the case of "We Can Work It Out." Both songs didn't really sound like anything either band had written beforehand, and featured arrangements more complex than either band had done before ("We Can Work It Out" took 11 hours to record, a record at that time for the Beatles). By now it should be clear the songwriting of both bands had taken a leap upward.
Though both songs are fantastic, I'm going to go with Let Him Run Wild (which has lately become my new favorite song). The arrangement is more complex than WCWIO, and the mood changes are simply ... spectacular. It opens with a couple of tense minor-7th jazz chords but quickly opens up into a sequence of major chords, which completely "breaks out" in the refrain, only to do a masterful segue back to the verses ("Guess you know I waited for you girl"). All that piled on top of a very well-done "layering" of instrumental lines. The perfect pop song, IMO. The Beatles tune is fantastic, but it doesn't lead me on the (nice) emotional roller-coaster LHRW does, it's a bit more even in that category.