I don't have the Mini - I have the iPad 4, iPhone 4S and an iPod Touch 4G.
In order of which leaves my house the most, from top to bottom, it would be the iPhone, followed by the iPad at a very close second, and the Touch at a pretty distant third.
Besides basic telephony, my iPhone is my go-to device for messaging (KakaoTalk) and exercise (Nike Training Camp) as well as keeping track of my spending (Moneywiz) and my to-dos (Clear and OmniFocus).
Basically the only times my iPad doesn't leave the house are when I'm out doing groceries or when I'm travelling. Other than that, it's always on me when I'm at work or when I just go out for social gatherings. For work, I use the iPad as a second screen for my MBA (Air Display), as well as reading various documents on the go, or if need be, make edits.
When my iPad is not in a work situation, it's my primary gaming device as well as consuming multimedia contents (Air Video, YouTube). I also use it a lot for my news habits (newspaper, RSS, magazines).
My Touch actually serves a pretty unique purpose given where I live. Since I jailbroke both my iPhone and my iPad, they cannot use banking apps made by the banks here, so I use the unjailbroken Touch for finance needs, like checking my balance, transferring money, or making online purchases. Online banking in Korea requires ActiveX, and it's just too cumbersome to deal with, since I need an installation of Windows. As such, the Touch takes care of that, saving me gigabytes.