Godzilla Vs. The Thing (1964)

Starring Akira Takarada, Yuriko Hoshi, Hiroshi Koizumi, Yu Fujiki, Kenji Sahara
Directed by Inoshiro Honda
(actor & director credits courtesy IMDB.com)

A giant storm transports an enormous egg to a Japanese city, which is claimed by greedy industrialists, but its contents are the progeny of Mothra, who will soon face off with Godzilla. 

Although the American title of this film leads you to believe there's a mystery behind the egg, its Japanese title was Mothra Vs. Godzilla and it becomes pretty clear that the egg belongs to Mothra early on, as soon as Emi and Yumi Ito reprise their roles as the tiny princesses of Mothra's island from the creature's first film.  Those hoping for a full-on battle between Godzilla and the flying moth monster may be disappointed as Mothra is weakened and dying during the battle, but there will be others who will carry on.  The filmmakers stage a clever strategic confrontation by Godzilla's foes with some pretty good effects, and the human cast are entertaining, with Takarada returning for his second Godzilla film, although playing a different character.  I haven't yet seen enough Godzilla films to estimate where this ranks in the series, although for me it's clearly behind the original, but still a fun entry, and one of the first to pair off Toho's different kaiju.

King Kong Vs. Godzilla (1962)

Starring Tadao Takashima, Kenji Sahara, Yu Fujiki, Ichiro Arishima, Jun Tazaki
Directed by Inoshiro Honda
(actor & director credits courtesy IMDB.com)

While Godzilla is escaping imprisonment in an iceberg, a pharmaceutical company captures King Kong on a jungle island, leading to an eventual clash between the two titanic monsters.

If you were expecting detailed animated monsters rendered with cutting edge special effects, this isn't the movie for you.  However, if you're a fan of Godzilla movies, and enjoy seeing men in monster suits crushing miniature buildings and vehicles, you should be highly entertained.  Although by this time in the Godzilla series any emphasis on realism had declined a bit, a number of other special effects are put to good use to energize the monster battles, including rear projection, giant mockups of Kong's hands, and what appeared to be some stop motion animation to bring a giant octopus' tentacles to menacing life.   The grim devastation in the monsters' wake is lightened by some comical human characters, and although the actual battles between the primary monsters take up a surprisingly short portion of the film, I was entertained well enough, and liked the picture better than the Kong-confined sequel, King Kong Escapes.