The iPad Mini's Guided Access lets you restrict the tablet to a specific app and even block some of an app's capabilities (such as Buy buttons) by drawing blocking ovals around their controls. But this new iOS 6 feature has to be enabled each time you want to use it and can be used for just one app at a time. It's fine when you want to hand your iPad to your kid for a specific purpose, but it's nowhere near as useful as the ability to set up separate environments, as the Kindle Fire HD can.
The iPad has a comprehensive set of parental controls that let you configure what your kids can access. Tech-savvy parents can even use Apple's free Apple Configurator tool for OS X to create and deploy profiles with such configurations to their kids' devices, as well as update them remotely (though we're talking supergeek parents here). Safari's private browsing mode lets parents access Web pages they don't want their kids to easily see, as this mode ensures no history is kept of the visited pages.
The Kindle Fire HD too has a solid set of password-based parental controls should you decide not to use FreeTime; these controls can also protect you should your device be lost or stolen. The Nexus 7 has no parental controls to restrict individual capabilities, just the ability to set a password for access to the tablet itself.
The bottom line is that the iPad Mini's iOS assumes that just one person uses an iPad (or iTunes), so it can be problematic to share freely. But it has the most sophisticated parental control options and the best corporate security capabilities. Android is even more single user-oriented and its parental controls are nonexistent, much less anything like the notion of separate user accounts. The Kindle Fire HD is designed for multiperson use and offers both good parental controls and adequate corporate security.
The security winner. For business security, the iPad Mini rules. For family security, the Kindle Fire HD rules.
Deathmatch: UsabilityNo matter what media tablet suits you, 7-inch tablets come with a fundamental usability trade-off. Small screens means small controls and small text. If you're middle-aged, don't be surprised if you need reading glasses, and don't expect to touch-type on the onscreen keyboards.