There can't be more of a apples and oranges comparison then when comparing the iPad mini to the Kindle paperwhite. They both perform well as readers however the Kindle is a much lighter platform. On the other hand Apple's iBook has many more features and makes reading in a stream a lot easier. One serious advantage that the iPad mini has is the audio. Listening to music on the iPad while reading is a great combo which the Kindle does not offer.
There are a few stability questions related to the iPad however. My iOS devices have been crashing. Furthermore the music player on the iPad has network issues when attaching an reattaching the local network.
It's still a tough choice when trying to decide which tool is going to end up in my briefcase.