Hmmm. It would be much easier to list where iOS has NOT been playing catch-up with Android for the last couple of years. Even with their proprietary hardware, optimized to run iOS only, the OS still feels dated and severely limited.
The only way to compare it's popularity would be to license iOS to other manufacturers and let the free market rules decide what's better. I guess they're too afraid to do that, despite the potentially huge monetary gains. The model has worked before (Windows, anyone? ) that has still has the lion's share despite the availability of other free OSes out there.
As much as people think iOS needs to play "catchup" how come my modern Samsung Galaxy S4 phone running latest Android updates needs to constantly ask me if I want to open a link in Browser or another app even though I click "Always" but sure enough every time I click a Wikipedia link it asks me again. Shit like this iOS doesn't put in front of the face of the user. And I love how the first thing a sales associates shows you how to do is installing CCleaner for Android because... ya know, even though it's got twice as much RAM as an iPhone it needs the extra help from software. Ummmm ya my experience with the last two Android phones has been trash while the iPad has been rock solid. You can forget that argument.
Personally, I think there is one thing Apple needs to prove that isn't on this list - especially in light of the smart home. They need to prove they can play nice with others. While they have done so well in the past, it would be nice to see them step up their game in this area once again.