Well, it all starts back on Beiju (aka Infant Island), an atomic test site in the South Pacific, where a team of Rolisican (aka American) and Japanese scientists arrive to study the curiously radiation-free natives, including the pair of cute foot-high twin girls whose sweet singing is really a cry for help to their larval insect deity as they are abducted by the shameless capitalist Clark Nelson who aims to pimp them out as a sideshow act and… well, you know how these things go. One thing leads to another and before you know it that insect deity, after swimming to Japan in caterpillar form, spins a cocoon in Tokyo Tower, hatches into adult form as Mothra, lays waste to the city, retrieves the girls, returns to Infant Island, and goes on to star in seventeen more films with approximately the same plotline, many with other monsters but none with Clark Nelson, who was shot by the police, thank God, that guy was a jerk.
So here’s a case where the 800-pound gorilla in the genre, Godzilla, actually approximates one. Well, King Kong would be closer, but we’re focusing on kaiju here − the Japanese concept of “strange beasts” that figure in all manner of tokusatsu (special effects-based) entertainment, notably the monster movies of the 50s, 60s, and 70s. In that world, every fanboy will tell you, Godzilla is first and best, strongest and angriest, most iconic and most thematically rich. He was originally a metaphor for nuclear weapons.
Can a giant moth really compete with all that? Well, yes, in fact, in Godzilla vs. Mothra (1964, Godzilla wins, but Mothra lays an egg with twin mothra-babies that trap Godzilla underwater in silk strands.) Of course, it’s not the death and life of these creatures beneath the seas or over Tokyo that matter, it’s their imprint on our teenage brains. And on that count, there’s really no contest.

Godzilla
Godzilla is a reptilian guy-monster whose main weapon is atomic fire. Mothra is a lepidopteran girl-monster who bites her adversaries on the tail. Yeah, okay, she whips up a pretty good hurricane with those wings, she’s got the silk-spray when she’s in larval form and she can communicate psychopathically with humans. Cool, very cool. But still.
Where Are They Now?
Mothra has not had top billing in a film since Rebirth of Mothra III in 1998. Godzilla pops up regularly across the pop culture landscape, most recently in the 2014 American film Godzilla, most head-bangingly in the 1977 Blue Oyster Cult song by the same name, and most dweebishly in the open source web browser Mozilla.
Afterthoughts
With possible rare exceptions along the lines of Alien, whose tentacular space creature was notably female, the truth is that until and unless humans evolve to the point where estrogen supersedes testosterone as the primary determinant of box office gross, ensuing generations of movie monsters in general and kaiju in particular will continue be led by the Godzillian, not the Mothric.
See Also: Rodan, Gamera, et al