Horace Dediu shows us total app installations from the iOS app store and the Google Play store. For a long time, Apple had a substantial lead despite Android's large market share thanks to a much higher level of apps per device. But though Apple still sells many more apps per device than Google the headline gap is narrowing.
This matters because of network effects. You want to buy a computing device that runs great apps. And people want to write apps for a platform that has lots of customers. The fact that iOS owners have been better customers than Android owners has clearly been a major consideration for a lot of developers in terms of where to spend their time and energy and that, in turn, has been a strength of the iOS platform. Now this doesn't distinguish between paid apps and free downloads, and so I think there's still a lot of evidence that the App Store is a superior marketing platform for most people. But if Android keep narrowing this gap, a key Apple advantage could go away quite quickly.
This is the strong argument advanced by the Church of Market Share—as both platforms mature and become "good enough", the larger platform will tend to win out due to network effects. I think the inevitability that some people attach to that idea is misguided. In theory, the huge operating surplus that iOS generates for Apple can and should be used to keep pushing the platform forward to make it better and better. But we haven't yet seen all that Apple cash deployed in a way that creates a new obvious qualitative edge for the company. That's the challenge going forward. In a competitive marketplace, Apple can't count on the app gap lasting forever.