I think both Android and iOS have their advantages and disadvantages. None is really better or worse than the other. Just different strokes for different folks.
Android
Advantages
-Greater hardware variety that caters to a wide variety of budgets
-Flexible and customizable, caters to both regular and power users
-Tightly integrated with Google's excellent cloud service
-No walled garden. It'll run any app that doesn't require root access. Not just ones Google deems kosher.
Disadvantages
-Lack of consistent OS updates on devices not made by Google. Samsung and LG are getting better about this, but it's still a huge issue with other device makers. Since manufacturers use their own custom builds, Google can't just push updates themselves.
-Security issues, exacerbated by said lack of updates. Holes on popular devices can take a long time to get patched, if they ever get patched.
-Might be some privacy issues due to some liberal policies on apps accessing your data
iOS
Advantages
-Apple's most excellent hardware and support
-Simple, secure, and safe to use for computer novices
-Lead development platform for large number of popular apps
-The App Store is much better than Google Play from my experience
-Regular software updates
Disadvantages
-Walled garden means you're limited to apps Apple deems kosher
-Hardware can be very expensive, especially off contract. Limited choice of handsets.
-Bloated software updates can slow older devices to a crawl, though Apple has gotten better about this in recent years
-Not very customizable
-Some of the built in apps (Maps, iBooks) aren't that great
-Forced use of iTunes to pretty much do anything between your device and computer