D.D.
I wouldn't go with either :)
My kids love minecraft and other games. I gave them the choice of iPad minis or iPod touches. We went to the Apple store to try them out, and they chose iPod touches over minis. They said that it was too hard to hold the mini and reach the controls for the games with their thumbs. The minis are easy for adults to handle, but not so easy for kids.
If you aren't so interested in games, but really want to read and watch videos/movies, then I'd go with the full size iPad to really see the videos and/or text.
Either way, get an Otterbox so it won't break if dropped.