At ~13:50, Davy is shown trying to feed a stuffed animal of a giraffe, repeatedly offering it what looks to be a piece of bread:
When he's unsuccessful, he smacks the giraffe onto the floor:
During the "Ticket to Ride" sequence of Help! (at ~40:01), Ringo is shown holding a small figure sculpted out of snow. It pokes him on the chest, and he pokes it on the nose:
After a few exchanges, he punches it:
I'm sure this isn't the most interesting or important comparison between the Beatles movies and The Monkees, but since I finally found this specific episode, I thought I'd make a note of it.
