The app's default for deleting messages is to move to Deleted folder first (local for POP3 or server side for IMAP), and delete from the server when the deleted folder is emptied (in AquaMail, long press the folder, choose from popup).
However, please remember that any mail app syncs with the server, not with other mail apps. Whether deleted messages disappear from the other mail app depends on how that mail app is configured.