Here's an interesting adoption plot of active users on a particular version of a major social networking app on the iOS App Store (In this case it was a Universal App). What it's interesting to point out is two different upgrade scenarios.
One scenario (Dark Green to Mustard) is where adoption is organic through the App Store and relying on the app store itself to notify the user. The second scenario (Mustard to Blue) utilizes an alert dialogue to let the user know a newer version is available with a direct link to the download in the app store.
Here's the comparison:
In a nutshell App Upgrade Adoption is slow, but you can certainly speed it up with an Alert when the user launches the app to let them know to upgrade to a new version.