Generally speaking, the pattern with Godzilla films seems to be that the ones where he’s the solo monster tend to be more serious and dramatic, while the ones that have him fighting other monsters are campier and more schlocky.
The big exceptions to this are the Roland Emmerich film, which doesn’t take itself very seriously, and GMK, which does take itself seriously, thought maybe not to the extent of the recent Toho films. I suppose the 2014 film also took itself fairly seriously, but not to the extent that the trailers made it seem.
In any case, the Monsterverse is all about the monster fights, so at this point, it’s clear that it’s leaning towards the schlockier side of things. I mean, it’s a franchise that exists because the former CEO at Legendary really wanted Godzilla to fight King Kong.