Research firm Ericsson has published data on the customer retention rates (i.e. how many people buy a new phone with the same operating system) for iOS, Android, and Windows (on mobile).
According to the data, loyalty to Android is higher than iOS, until Apple releases a new iPhone. Older iPhone users then become less likely to buy Android and buy a new iPhone, while Android users increasingly jump ship.
The Ericsson data measures Q3 2015 — the quarter when Apple released the iPhone 6S — showing that the percentage of users who swapped an iPhone for a newer iPhone jumped to 4.5% from around 1.1%. The percentage of Android users who went from Android to iPhone doubled to 0.6%.
For the majority of the year, when there isn't a new iPhone, user loyalty sits at 82% for Android and 73% for iOS. Around 0.3% of Android users switch to iPhone and about the same go back.
Here is the graphic showing loyalty before a new iPhone is released:
And after a new iPhone is released. Notice how iOS users rush to upgrade:
Windows has the lowest retention rate, losing around 2.5% of its users to Android and iOS after a new iPhone is released.