If Joan is at the peak of her powers (al la Miss Cosmos) she rape stomps.
If we're talking more classic era power level, or how her power downgraded after she lost the Miss Cosmos upgrade, then the stomping goes the other way.
If its Joan after one year later and not "miss Cosmos" level then its a good fight that can go either way depending on how seriously Joan is treating the fight and if she's going all out (for example how she delt with her imposter).
She allowed herself to be completely and utterly destroyed maintaining only a consciousness from which she simply reformed into a completely new higher evolved life form. At her peak (i.e Miss Cosmos level) she's in the league of (slightly below) Molecule man and there is literally nothing Majestros or anyone below skyfather could do to harm her.
Pre one year later she was a very basic matter manipulator who hadnt done anything really complex. Post 1 yr later she was extremely accomplished and had extensive control over her own molecular make up. She allowed herself to be old (to age) and could make herself young and vital again at a thought. She could turn peoples organs to glass easily at will. With a mere thought she could make Majestros become fragile china that is easily smashed and no longer invulnerable. Sometimes she acyed this rashly/harshly but notnconsistently. As I said would depend on her mindset.
IIRC, Miss America is like Uncle Sam. They are America, given human form or whatever. They can't be fully killed, unless the spirit of America is killed.
No thats not the case at least not in current post coie canon. Pre crisis she was spoken to by the statue of liberty and given her matter manip powers to protect democracy. In Young All Stars early issues it was retconned that the talk from the statue was a hallucination ehen she was drugged and used as a test subject by project M (where the young all stars took their captured Fury to).