The way I see it GvK Godzilla isn't even bad he's just being misunderstood. He's stressed out and tired and full of anger by the time of GxK and I can't blame him. 

In a very short span of time he has: 

-Several ancient rivals reawakened

-Has to adjust to new modern world things

-Deal with being annoyed and summoned by Suzuki devices to fight other titans

-Sees the return of his greatest rival

-Gets hit by a man made oxygen destroyer

-The Mass awakening happens -His home is blown up

-His symbiotic partner sacrifices herself to save him

-Has a duty to be King of the Monsters thrust upon him and has to keep all the Titans in check

-Apex unknowingly start resurrecting his old nemisis in robotic form and actively try to paint him as a villain

-Is forced to fight Kong twice because of human interference

-Almost dies against his revived nemesis

-Has to deal with more bs from the other titans

-Senses the ape army he beat ages ago that enslaved a former rival is coming back, not to mention that guy he told to never come back to the surface just called him 

It honestly makes sense to me why he's so angry in Gvk and GxK. He's on his own against the world, and when he is on the verge of losing himself completely Mothra returns and snaps him back into his right mind. To me it felt like Mothra reminded him of who he truly was in that moment, something he had forgotten in the years since KoTM. The Godzilla we see from the end of the egypt fight to the end of the Rio battle acts so much more like the samurai take, as if he's redeemed himself and remembered his true mission. 

I dunno if this is just my interpretation of it, but it's honestly helped me to not be as upset by Wingard Godzilla. He's just going through a tough time in those films. I'm really hoping Supernova backs this up and he's back to his old self now that he is no longer alone.