The only part of Office that you can ONLY have one version of is Outlook - it WILL NOT allow two versions to be in stalled on the same machine.

I would advise doing a clean install - go to the Microsoft site and get the clean uninstaller (search: remove office) and remove both copies of Office first - then install 2003, followed by a custom install of 2007 (this will allow you to choose which versions of each application you wish to install.