This is a match idea Hulk created.
Godzilla excels in monster vs monster fights. Giganta's track record against foes her size is very sparse with no examples to my knowledge. Godzilla will have the definite fighting skill advantage. Since he also has claws, teeth, and a tail; he has more natural weaponry and can put out more hurt in melee. Then there are his more esoteric powers, his breath ray is not the only thing he has; though it has been rated as pumping out megaton firepower per second, perhaps more for the incarnation that was doing all sorts of wonky stuff to a black hole he shot at. He also has the nuclear pulse; which creates a blast of force centered around him that while capable of causing catastrophic damage; is best used for forcing a grappling opponent to let go.
He also has flown by shooting his breath ray at the ground and using it as a thruster, he has randomly turned one of his weaknesses (electricity) into something that makes him stronger, he has defied such silly things as "obeying any sort of law of motion" by getting on his tail and sliding at high speeds for a drop kick (no, it doesn't make any more sense in context), randomly out of freaking nowhere turned Magnetic enough to drag god damn Mechagodzilla out of the sky over several miles, can spit explosive radioactive fireballs, has ran so fast he became a blur and when he finally decided to get serious; easily tagged a hypersonic flying fragile speedster and utterly demolished her in a few hits, oh and he's survived a meteorite impact, a nuke to the face, and a god damned Black Hole.
Godzilla's silver age days made him the Superman of moviedom. He laughed at such silly things as making sense, having internal consistency, or a defined power set and instead had whatever the hell kind of abilities he felt like. He once even talked, in plain English.
^ Destroys 120+ meter diameter meteor with his atomic breath that was sent by aliens and moved many times faster than real life meteor. Both Godzilla and the monster inside the meteor survives the city buster explosion undamaged, still standing
^ Monster X tanks Godzilla's concentrated nuke beam to the face undamaged at 1:09.
^At 2:22-2:30, Monster X's beams are equal in power with Godzilla's.
^At 2:31-2:44, Monster X Transforms into it's second form, Kaiser Ghidorah.
^From 2:45-3:13, Kaiser Ghidorah's beams over power Godzilla's beams in a beam fight. The video shows a shortened version of what happened, but Kaiser Ghidorah repeatedly uses his gravity beams on Godzilla around over over a minute. All they did was stun him and leave temporary burn marks that lasted a few seconds. Kaiser Ghidorah finally decides to pick Godzilla up and uses his powerful energy draining ability to KO Godzilla. A weaker version of Ghidorah from the 1960s, a two legged version of Ghidorah called King Ghidorah, had destroyed an alien civilization on Venus.
^From 3:14-4:07, Osaki transfers his Kaiser powers to Godzilla, Godzilla's energy pulse was so strong and overpowering that Ghidorah couldn't absorb it and was forced to let go, then Godzilla blows one of Kaiser Ghidorah's heads off with his normal beam, forced Ghidorah to cut one of his other heads off, kicks Ghidorah around for awhile, then one-shots the rest of Ghidorah's body using his red spiral ray beam.
Base Final Wars Godzilla's Normal Atomic Breath which had destroyed a super fast meteor, city busted and moved a mountain sized mothership < Monster X's durability which tanked his breath multiple times. Monster X had no bleeding wounds after 20 minutes of fighting Godzilla. < Kaiser Ghidorah < Kaiser Godzilla's Normal Atomic Breath < Kaiser Godzilla's Red Spiral Atomic breath.
Godzilla with Kaiser powers = The most recent Toho Godzilla and one of the strongest versions.
Another version can survive a miniature black hole, and another one has enough nuclear power in his body to at least destroy the Earth one time.