I don't think mail actually comes in while mail is closed - on the mac, when you apparently close mail it is still actually running and, if set for automatic checks, will check for new mail every whatever you set. Look at the mail icon in the dock - if there is a little triangle below the icon it is still running. New mail is signified by a little red circle with the number of new messages in it. It's more than minimised (which would put a miniature icon portraying a mail page in the dock) but it's still open. To quit completely you have to press Mail, quit mail.
You can set outlook to send/receive automatically too but I don't think you will get mail unless the program is running unless you are on an exchange server.