You use Final Cut Pro to edit video.
When you have done that, you compress it and bring it into DVD Studio Pro.
You use DVD Studio Pro to author your DVD, including building the menus. If you want your DVD menu to have a live video background, by all means make that part in FCP them import it into DVD SP as a menu background. Place the menu controls on top using either elements from the DVD SP presets or graphics created in Photoshop.