The Android or iPhone software platform is more than just a core operating system. And really, the differences in their core operating systems are one of the least important factors to users. Both use a Unix-derived kernel and operating system environment that few users will ever even see. Android phones happen to use a Linux kernel while the iPhone uses the same Mach/BSD Unix kernel as Apple’s desktop Macs.
In the big picture, this doesn’t really matter much because neither smartphone platform provides any real access to this layer (either to users or developers), and neither phone platform is designed to run desktop software developed for Linux PCs or Macs. Both systems are examples of well regarded technology that is fully capable of supporting the needs of the smartphone environment above the core OS.
The actual platform environment that matters to users on Android and the iPhone exists well above the core operating system kernel. This is where applications run, where security is enforced, and where the business model behind the smartphone impacts what users can and can’t do.