Sure, Android can perform this action all by its lonesome, and there are rumors that iOS 9 may include such functionality, but until then, iOS users can use Opener. This $1.99 app (£1.49 in the UK, AU$2.49 in Australia) lets you open links in their corresponding app, skipping the annoying Web view along the way. Opener makes it so when you come across an Amazon link in Safari, for example, or an Instagram link in Twitterrific, you can quickly open those links in the Amazon app or the Instagram app, respectively.
Opener provides two methods for opening a link in the right app. You can copy the link and then launch Opener, which will offer to open the copied link in the right app.
A better way is to use Opener's action extension that adds the app to iOS 8's share sheet. (Opener provides step-by-step instructions on setting up the action extension.) The action extension saves you the step of needing to open the Opener app to get a link to open in the right app, but you will need to be using an app that supports iOS action extensions. Safari does and so does Twitterrific, but the Twitter app does not.
With Safari, the process was not as smooth as I had hoped, mainly because I had to open a link in Safari -- thus, viewing the Web view I was trying to avoid -- before I could access the Opener action to kick the link out to its app. It worked better on Twitterrific, where I needed only to long-press on a link to access the Opener action. In either case, when you tap on the Opener action button in the share panel, an Open In panel slides up asking if you'd like to open the link in its app.
You can skip this last step of needing to tap the Open In panel, however, with Opener's auto-open option. When the Open In panel pops up, long-press on the app listed and it'll offer to open automatically such links in the future. With auto-open enabled for an app, you will see the Open In panel for a split-second after tapping the Opener action button before a link's corresponding app opens.