We know that dragons emerging from water symbolize inconceivable chaotic forces:
The motif of Chaoskampf (German for “struggle against chaos”) is ubiquitous in myth and legend, depicting a battle of a culture hero deity with a chaos monster, often in the shape of a serpent or dragon. The same term has also been extended to parallel concepts in the religions of the Ancient Near East, such as the abstract conflict of ideas in the Egyptian duality of Maat and Isfet.
The origins of the Chaoskampf myth most likely lie in the Proto-Indo-European religion whose descendants almost all feature some variation of the story of a storm god fighting a sea serpent representing the clash between the forces of order and chaos. Early work by German academics such as Gunkel and Bousset in comparative mythology popularized translating the mythological sea serpent as a “dragon.” Indo-European examples of this mythic trope include Thor vs. Jörmungandr (Norse), Tarhunt vs. Illuyanka (Hittite), Indra vs. Vritra (Vedic), Θraētaona vs. Aži Dahāka (Avestan), and Zeus vs. Typhon (Greek) among others.
Therefore, when two such Lovecraftian leviathans come out of the ocean and do battle amidst Neo-Tokyo it represents the unpredictable war of two supernatural forces with unclear goals and alien psychologies.
Art by Andrea Boloch
This is a pretty simple mythical trope, but a fun one. Since the fates of the humans and their city are more or less governed by accident–depending on what fraction is wiped out by collateral damage, which monster is eventually victorious, and that monster’s ultimate disposition–we can interpret these kaiju battles as representative of a fatalist philosophy. A virtuous man in a world where such monsters exist will engage in a hedonistic fast life strategy most of the time, generally keep his head down to avoid attracting the attention of alien agamids, and run away screaming when shit occasionally hits the fan.
An interesting variation is when one or both of the monsters is manmade, symbolizing the powerful but often monstrous ideological systems we incorporate to cope with unknowable horrors from beyond. These themes are surprisingly flexible. In G Gundam the countries of the world send their champions to fight in a mecha tournament instead of fighting wars. In Evangelion humanity sends its champions to fight Lovecraftian horrors in mechas that turn out to be Lovecraftian horrors themselves.
In Big O the monsters coming out of the sea are themselves man-made mechas.
These represent variations of the underlying philosophy, but in the final analysis these robots are still human cultural heroes made of lightning, just with more ratiocination.
If you’re looking to play with this a bit more, please note that it puts a new spin on the emergence of four kaiju horsemen in the behelit myth.