There is nothing more obvious than the fact that iOS and Android are competitors and are pretty much the only ones in the smartphone market as it stands today. Though iOS had a few years of head start to Android, Android soon caught up to iOS and eventually beat it in the market share by a huge margin, globally. Most recent data (via BusinessInsider) suggests that the trend that has been valid in terms of market share when it comes to smartphones has not changed much in the last couple of years. That is Android has close to 75 to 80% while iOS has close to 18 to 20% of the global smartphone market.
Everyone in the Apple blogosphere (including me) has always argued that the market share alone is not the complete story and it is only wise to compare the profit share as well in the smartphone market as Apple doesn't typically play in all the smartphone markets that Google does. In terms of profit share, Apple has trounced Google (by a bigger margin than Google has trounced Apple in marketshare) for quite a while now. The recent data (via AppleInsider) on the profit share of iOS v/s Android in the smartphone market suggests the same trend holds true. Apple makes almost 9 times more money that Google from its mobile devices.
But just like how, concluding that Google is winning the smartphone race based on the market share data, is absurd, it is equally absurd to conclude that Apple is winning this race based on the profit share data. The missing parameter in this context is the objective of each of the two companies for their mobile operating systems. Apple's is a product company and its objective is to make the best products (according to it) and the boat load of profits it makes is just a by product or a confirmation that its doing its job. Google's objective with Android is to be omnipresent or be installed in the most number of devices as possible across the globe, to increase is install base for its ads and other related businesses. So based on these, shouldn't we conclude that both companies have succeeded in their respective missions? I think so and this statement is true at least as of today. But the biggest loser in this race is and has always been Microsoft. It doesn't even feature in some of the tables and plots above with a non-zero value!
Note: It might be wise to look at micro markets for a more apt comparison of these two mobile strategies. Like how Apple is gaining and maintaining a strong foothold with its iOS devices in the Enterprise market (via VentrueBeat) or how Google is paving itself a nice niche over taking Apple in the educational market (via BusinessInsider) with its Chrome books (I still think Chrome OS is the future of Android by the way).