I don’t see anything that can permanently kill Arcueid. Sailor Moon doesn’t have Existence Erasure she has resistance to it. I doubt transmutation would work unless it affects her soul also I don’t even think she has access to it in her 4-B key. Unless she destroys her soul I don’t see anything that can kill Arc permanently.
I guess Archetype Earth turns her into energy and wins?
Sailor Moon’s weaknesses “Merciful against her opponents and often does not use full power against her enemies”. While AE is very arrogant that’s mostly because she is so far above everyone else in Melty blood but even then she plays to win. So against SM she will go matter manipulation and transmutation first.
Good ..... I'm going to bed and I can not answer for a moment, so I'll tell why Usagi has a better chance of winning
Firstly the attack that it will be able to eliminate Earth Earth can also eliminate it with Matter / Transmutation but:
I do not think she can use this ability From as far away (4km maximum distance)
Her behavior, although as I have been told, she is arrogant, she will probably be amazed or shocked at the huge gulf between them, anyway, she will destabilize, which shortens the chance she attack first
Sailor moon's Silver crystal warned of danger, so she'll know that Earth is getting ready to do something
No she won't. Her attitude is the same as the Crimson Moon, and he knows that there are beings stronger than him. Also in Kagetsu Tohya when Roa mentioned that Altrouge surpassed him in a way because she has Primate Murder Crimson Moon didn't care too much.