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.