In 2016, this is impossible to achieve via Javascript alone
You can still use the approach on Android, but Apple made changes in iOS 9.2 that mean this is essentially useless on iOS devices.
How it used to work on iOS
The way this was done in the past was to attempt to open up the app in Javascript by setting window.location to the custom URI path that you wanted.
window.location = “imdb://title/tt3569230”;
App not installed
The problem with this is that when the app is not installed, it shows a ‘Cannot Open Page’ error. I’m sure you’ve all seen it. It’s the bane of deep linking. There was a glorious period during iOS 7 and iOS 8 where it was possible to bypass this, but the golden age has passed.
In order to avoid this, you had to add some Javascript to your page where you would redirect away to the App Store. This way, the user was not left with an error on the screen.
window.location = 'imdb://title/tt3569230';
setTimeout(function() {
window.location = 'itms-apps://itunes.apple.com/us/app/imdb-movies-tv/id342792525'
}, 250);
App installed
When the app was installed, it would display the modal below, prompting the user if they want to open the app:
What happens now is that in iOS 9, Apple changed the Open in "[app]" modal from a Javascript blocking modal to a non-blocking modal. This means when you try to open up the app via a Javascript redirect to a custom URI scheme, the modal will no longer block Javascript from executing, with the result that the fallback redirect to the App Store will execute immediately before the user can tap the 'Open' button.
At Branch.io (full disclosure: I'm on the Branch team), we saw this coming in the iOS 9.2 betas and were hopeful that our Apple radars (bug reports) and influential partners could motivate Apple to resolve it before release. Unfortunately for iOS developers, it was not to be. Apple’s response to our concerns made perfectly clear what they wanted everyone to do: adopt Universal Links.
Solution for 2016
The only way to have a single link that works everywhere (including routing into apps if they are installed or to fallback web URLs if they are not) must include using Universal Links on iOS. Of course, Universal Links aren't actually supported everywhere in iOS yet, so there are specific edge cases where custom URI schemes are still required (Chrome and Gmail being two big examples). You'll need to detect these and build custom handling.
Most companies don't have the resources to devote a full-time engineer (or two) to this, which is why Pinterest, Tinder, Airbnb, Jet.com, Yummly, etc., have all adopted linking platforms like Branch.io or Firebase Dynamic Links.