iOS currently offers no way to set third-party App Store apps as default on the iPhone or iPad. In other words, tapping on a link opens Safari and you can't make it open Chrome instead. Choosy, an open-source framework by Substantial's Alex Novosad, aims to let developers offer a work around in their own apps:
All of this relies on UIApplication's canOpenURL method. (Oh the things we could do if we had two API methods!) We store a list of URL schemes and their building blocks for each app on a server (in a GitHub repository right now), categorizing apps by type. Choosy downloads that info as needed. Developers code to an app-agnostic interface where they just specify the type of app they are linking to/trying to interact with, and pass in a list of parameters. Choosy maps those parameters to the parameters supported by each app and builds app-specific URLs.
Since it's not being implemented by Apple it's not system-wide. That means it only works in apps that do implement it. Yet work-arounds like x-callback have already been used with great efficacy by apps like Launch Center Pro and Drafts. If a few incredibly compelling apps appear that use Choosy, or if a critical mass of apps embed Choosy, who knows what could happen?
Apple could announce their own way of handling default apps in iOS 8 or some future version. Until then, developers who are interested in default apps can check out Choosy, and anyone who wants default app functionality in their favorite apps can encourage developers to check out Choosy and see if it works for them.