I do use the Kindle Paperwhite on nearly a nightly basis. After staring a backlit screens all day long, I still find the Paperwhite nice on my eyes before I go to sleep. I’m also about to take off to a beach for the long weekend and it’s definitely great in that setting.
Overall, the Kindle inventory and lending library aspect seems better than iBooks, but I actually like the look of iBooks better. Kindle has been getting better at removing some of the cruft in the reading experience, but there’s still more to go.
Long story short: I don’t really use the iPad mini for reading books, but I use it all the time for reading the internet. I use the Kindle Paperwhite for reading books. We’ll see if a retina iPad mini changes that equation.