The scene in which Spike the Dog saves the girls from being trapped by one of this movie's antagonists is similar to the scene where Mumfie is saved from being trapped by The Secretary of Night, since both end with the trapped characters hugging the person who rescued them.
When Whale is freed from the boat he is underneath, he says "Oh, joy! Oh, rapture!", a reference to this musical's song "Oh Joy, Oh Rapture Unforeseen". Mumfie also whistles a bit of "Never Mind The Why and Wherefore" when visiting the Secretary of Night.
There are multiple similarities with the stories told in both movies. First, the main character makes friends on the way. Second, the first friend the main character of each story finds is a scarecrow. Third, there is a character who wants to go home. Fourth, the main villain of each story wants to capture the protagonist. And finally, the characters' mission is to go to a special land ruled by a powerful ruler.