For an occasional player looking for "just another game", the pocket version (~$5) is fine.
If your child would like to be a serious Minecraft builder and part of the community, that requires the broader capabilities of the computer version (about $30), plus your willingness to enable/ allow a fair bit of downloading of mods, plug-ins, etc. Why on earth would you ever want to do that? What makes Minecraft interesting is that everything is open source code, and there are millions of people all over the world building things in it, modifying code, creating adventure maps, puzzles, and all sorts of crazy things (you can get a taste of what people are doing in this description of Minecraft maps - just one of many types of stuff people create and post for anyone to download:
http://minecraft.gamepedia.com/Tutorials/Custom_maps). It's an incredible incentive to dive into the code, learn to program, and participate in some real cool stuff that's way beyond just playing another video game.
Obviously, however, this works best if you have someone in the house willing and able to supervise a high level of on-line interaction, including helping your child find kid-friendly servers if she wants to play somewhere with her friends, and safe sites to download mods from. I say it's totally worth it - but of course, easy to say, since DH is the tech support around here!
