If it ain't broke, don't fix it. Sega essentially took Saturn's 3D Controller, kept what was good, improved what they could, and added some new extras to boot.
The thumb stick, styling, and ergonomics were improved. The confusing six face buttons were replaced with... exactly the same 4 button configuration as seen on the Super Nintendo controller. And what's this? That looks like a cross-shaped control pad! I'll have to assume that they got around Nintendo's patent by the fact that this pad's internal mechanism is fundamentally different than Nintendo's. The controller also sports two shoulder triggers similar to ones on Saturn's 3D Controller.
The big new innovation is the expansion bays. Similar to the bay underneath the Nintendo 64 controller, except that there are two of them and there is a window on top of the controller to see what's plugged in... because, instead of using simple memory cards, the Dreamcast's "Virtual Memory Units" actually have their own simple CPU, LCD screen, control
pad and buttons. The LCD can display information during
game play, or the VMU can be unplugged and used separately.