None. They have different uses.
Ubuntu Tweak is a Management Tool software, which happens to have an menu for installing popular applications. It has menu entrys that allow tweaking windows buttons, cleaning cache and so on. I personally think that Ubuntu Tweak main focus is allowing easy configuration of the system, not installing apps, and this should be the focus of future versions of it. So yeah, I don't think it'll overlap the functionalities of Ubuntu Software Center.
Ubuntu Software Center is a Application Install Software (front-end to apt-get) which allow you to install/remove ANY applications in your computer. I personally think that Ubuntu Software Center focus is to make easier to install/remove/manage software for your system. I think it's headed to archive a experience of a "Iphone Store" for the Linux Desktop, which we can see as they are trying to synchronize applications installed on the system and pushing payed apps on the Software Center.