Microsoft officials have said that the Cortana apps for iOS and Android won't be as feature-rich as Cortana on Windows and Windows Phone, as it won't be as tightly integrated with the operating system. For example, on iOS, the "Hey Cortana" wake-up feature won't be available, at least not initially.
Update: Here's the Microsoft blog post announcing availability of Cortana on iOS and Android. In it, officials say the Cortana app is available today in the U.S. and China for iPhones on iOS8 and up and Android 4.1.2. It will be available in the U.S. on OnePlus One powered by Cyanogen OS with the 12.1.1 over-the-air update later in December. The Cortana app will be available on more Cyanogen OS-powered devices next year.