About 99% of mail providers use the IMAP protocol nowadays. The Mail app is essentially a window into the contents of your mail account, all of which remains in the server. If you're using Microsoft (Hotmail, Exchange, Outlook, Office365), check in Settings / Mail, Contacts, Calendars / <your mail account> / Mail Days to Sync that it is set to No Limit or something sufficiently far back.
BTW, was the backup you made in iTunes encrypted with password? If not, many of the fine-tune settings such as these as well as passwords do not get saved for security reasons. If that is the case, you still have the old iPad and you have not done things in the new that you don't mind losing, maybe it would be more convenient to redo the backup, ensuring it does have a password this time, wipe the new iPad clean and redo the Restore.