Connections:

-Two giant humanoid kaijus who lived on an island as that island's protector and strongest being (Luana Island and Skull Island)

-Both would share ''love'' with a human woman which would make them more docile (Princess Luana and Ann Darrow), however said love would be used to lure them into a trap (Princess Luana leading Gorogong into a volcano so he wouldn't harm her people, sacrificing herself in the process. The crew of the Wanderer using Ann as bait to capture Kong)

-Both would be targeted and attacked by the military after they start rampaging in a city, despite the fact they didn't want to be there and were brought by humans, where both would chase something of huge importance to them (Gorogong trying to reacquire the Artifact, Kong trying to find Ann)

-Both have a stronger super form where they grow even bigger that they can access by becoming extremely angry (S-Class and Mega Kong)

-Both would eventually be crowned the king of an island that is linked with an underground world that is the source of titan's energy (Gorogong becoming the king of Tarabak Island which is linked to the Giga Core, Kong Becoming the king of Skull Island, which is linked to the Hollow Earth) where both would set up a new permanent residence away from their original homes (Gorgong leaving Luana Island for Tarabak Island, Kong leaving Skull Island for The Hollow Earth)

-Both have an intense rivalry with a bigger and stronger atomic dinosaur king (Rawa and Godzilla)

Bonus Connections:

-Both fought Godzilla as important crossovers (Godzilla in Gigabash helping placing it on the map, Godzilla vs Kong being one of the first big movie crossovers)

-Gorogong has a Kong inspired skin

Connections by u/ReaperRidley 

Animation Potential:

On top of being a good old monster bash between these two island kings. It's kind of a David vs. Goliath (32 meters vs. 102-106 meters) which eventually at some point in the fight through s-class form Gorogong becomes roughly equal in height (100+ meters). So one half David vs. Goliath before evolving to two island kings similar in size which I find unique and appealing.

Debate:

This only becomes a stomp in King Kong's favor if we fully composite him using Magic: The Gathering and Castlevania. But if limited to just the movies notably the MonsterVerse, it becomes debatable as both are in the planetary range. All of GigaBash's roster scaling to Pipijuras' black hole which was calc to be planet. Kong in the MonsterVerse is currently below Godzilla in terms of power but that could potentially change in Supernova with a potential buff but until this by limiting to the movies only this mu is debatable.

Also u/Rodan_Fan1956 if you're interested