Captain America is back to fight again, but this time he’s up against the legendary Godzilla! Godzilla has his atomic breath and can use it to take down many opponents. Of course Cap has Mjolnir and with it not even Godzilla can take him down. Mjolnir is just far too powerful. Captain America wins.
DReager1.com 
Stomp! Cap. dies by being stepped on by accident.
Remember, he has Mighty Mjolnir! With it he could do some geavy damage to Godzilla
The Marvel Godzilla took on the combined might of the Fantastic 4, Thor and the Godzilla Squad in one comic and Thor himself compared Godzilla’s power to that of the Midgard Serpent, if not greater. Thor couldn’t beat Godzilla, Captain America won’t be able to do it either. Also, having Mjolnir won’t do him much good, Thor has super strength to back up his hammer, Captain America is far far weaker than him. Godzilla won’t feel a single thing from Mjolnir if Cap wields it.
Cap still has the Supersoldier serum so his throw won’t be downright weak. Also he knows how to run and can safely dodge Godzilla for a while. After spamming Mjolnir for a while Cap should take the win.
As for the comic…..I didn’t agree with most of it. All of the characters weren’t using their abilities too the fullest and should have made quick work of Godzilla. I like Godzilla, but I’ve never considered him too be as powerful as these comic book characters
Captain is strong but compared to Thor, it’s nothing big, especially not if compared to Godzilla.
Cap can run all he want but he won’t escape Godzilla due to his sheer size advantage. If we take Final Wars Godzilla, it’s even worse. Final Wars Godzilla is super fast, he can run a mile in a few steps alone.
Also a fun fact I learned from watching Avengers Earth’s Mightiest Heroes: focused radiation can rip inertia of an object in motion. Radioactive Man stopped Thor’s hammer by blasting in casually with a stream of radiation, rendering it silent. Godzilla emits massive amounts of Radiation alone, any blast or pulse from him would render Mjolnir silent, not to mention it would kill Captain America after a few minutes of exposure.
I don’t agree with your comic comment.
The Fantastic 4 have no way of stopping Godzilla directly. Thing can’t stop Godzilla when he was shrunk down so a full sized Godzilla is out of the question. Invisible Woman’s barriers won’t stop Godzilla either. Hulk managed to break those barriers with brute strength alone, something Godzilla can do easily. As I already said in another thread, Godzilla is nearly immune to heat so Torch won’t be burning Godzilla. Even if it works on him, Godzilla has regeneration on par with the Hulk, so Torch will exhaust himself on Godzilla.
Mister Fantastic’s only hope is to send Godzilla into another dimension, something that might work but even then, it’s not certain. Godzilla destroyed a black hole in Godzilla vs Megaguirus so he could probably destroy the dimensional portal Reed would use on him.
Thor is the only one with any sort of chance against Godzilla but as he said himself, Godzilla is more powerful than anything he ever faced before. Why wouldn’t he go full power of Godzilla? I understand he won’t attack the Hulk at full power since he doesn’t want to kill Bruce Banner but Godzilla isn’t human nor his friend so he needn’t hold back. I say those comics are accurate but not long enough to portray an implausible fight so I’ll leave it be.
Needless to say, Captain America isn’t one of the strongest Avengers, he’s just a very influential man.
Well I agree that Cap can’t compete with the other Avengers. He’s barely above human and one of my least favorite Marvel characters. But props where props are due. With Mjolnir and his super shield he can take on Godzilla. Godzilla is huge, but that’s a bad thing. He could try to step on Cap, but it will be easy for Cap to dodge by skittering around him.
Thing could just barrel into Godzilla while Human Torch speedblitzes him from all side. Invisible Woman can make a bubble inside of Godzilla and expand it. Mr Fantastic can take out one of his cannons. I think you may be underestimating the FF.
Thor just needs to spam the elements or keep on smashing Godzilla.
Still Godzilla and Cap are to be feared!