
This is a pretty hard choice. I have no idea who to pick.

MonsterVerse KG.

Which King Ghidorah?
Edit: Nevermind. I see that's been answered.

Legendary Ghidorah wins. He can take Legendary Godzilla's atomic breath with no apparent injury and can lift the 100,000-tonne creature easily. Shin Gojira has no apparent combat abilities except for firing beams, which are inferior to Legendary Godzilla's mantle-penetrating beams. Ghidorah will just knock Shin down and lift him up into the air before dropping him to his death.

Ghidorah is more intelligent (he has 3 brains), while Shin Godzilla doesn't think that much (he acts more on impulse). Ghidorah is also more agile and can fly, while Shin is slow and lumbering. So I think Ghidorah has more of an advantage.

I'd probably say that Godzilla would come out as the winner. Ghidorah has speed and agility as well as three brains to work with but Shin evolves on the spot almost. Plus Shin and G-Earth have thee most strongest Atomic Breaths, Legendary Godzilla didn't even leave any burn marks with his Atomic Breath against Ghidorah. I'm sure Shin would slice Ghidorah in half with it's atomic breath.

Actually In a line in the movie, it’s stated to be just as smart, if not smarter than humans, and gets more intelligent every evolution. And because we haven’t seen it’s final form, I wouldn’t judge that quite yet, So...
I think that Shin Godzilla’s Dorsal Beams are modified nuclear pulses from Burning G.

King Ghidorah. Through my knowledge, (I think) Godzilla has never beat Ghidorah nor Mechagodzilla without some sort of help.

To be fair we are comparing KG against a kaiju that doesn’t exist. The fourth form of shin godzilla isn’t its final form.

Oh yeah, I guess that’s true. Is there even going to be a final form? Or will it just keep mutating until it’s overpowered?

It is already over powered, Toho says it’s the strongest godzilla. Except for godzilla earth

Oh ok.

A thought struck me, what would a finally evolved Shin Godzilla Look like?

SarcasticGoji,
I think part of the point of the 2016 Godzilla is, unless there's something around him deemed superior, he's never done evolving. Kind of horrifying.

he's like
'HOLD ON IM NOT DONE YET'

that’s why Godzilla ultima seems more powerful a kaiju than shin to me. It does have a final form which is supposed to be the best. Shin adapts to its environment and this has potential but can be exploited to make it lose traits, and its change isn’t instantaneous.

I was going to vote KG, but what swayed me to Shin G was his atomic breath and his ability to discharge it from his spines. Shin G is very slow, but durable. I'm sure he could take KG's beams, and if KG tries to wrap around him like how he did with Monsterverse G, Shin's rays are going to seriously hurt him.