How to stop Mail.app filling up with downloaded mail
Why don't you move all your existing e-mails from Mail to Outlook, instead of having to switch between two applications to do it? This article suggests that Outlook might be able to do that directly from your hard drive.

As @Pratika Rana pointed out in the comments, you can also turn off autodownload of e-mails by account: in the Mail preferences (Mail -&gt; Preferences... in the menu bar), select the account you want to modify and select the Advanced tab. The Include when automatically checking for new messages should turn off automatic downloading of new e-mails, while leaving your account active and existing e-mails untouched, while still giving you the option to download new e-mails manually if you go back to using Mail in the future.