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One moves it to the trash and the other essentially saves it.

I prefer deleting. I don't need emails cluttering up my accounts by archiving them.
 
Depends on your mail provider. Gmail is based on Google’s insane server database tech, and there's no performance penalty for keeping archived every mail you're ever going to get. I personally archive and delete only mails I definitely know I won't need ever (newsletters etc)
 
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