Due to the large number of fast-song megahits both bands were creating in 1963 and '64, I'm going to add a previously unscheduled contest.

These are late '63-early '64 recordings.
Contest #4: Battle of the Late 1963-Early 1964 Teeny-Bopper Fast-Song Megahits, Vol. 2
"Fun, Fun, "Fun" - recorded January 1964
"I Want To Hold Your Hand" - recorded October 1963
My verdict: Unlike the previous fast-song megahit comparison, I like the Beach Boys song better.
Be sure to cast your own votes!