If they are both aliased, it is irrelevant - if they are mailboxes, mailboxes are, by definition, associated with domains.
The end result, either way, is that the alias should forward to wherever you have it set to forward.
If you are using IMAP, you will have to migrate the one mailbox to the other to keep all the mail intact. If you are using POP3, it shouldn’t make any difference - just download everything to your client computer, change mailboxes/addresses as desired, set up your client for the new mailbox, and keep on going.
You can export he old account’s mail in the client, and import it into the new account if you want, or don’t (the email should still be available in the client under tho old account).