Disclaimer: Just my $.02.
I work extensively every day with iOS and Android devices (I work in the wireless industry), and in general, my feelings on each can be summed up in brief contrasting lists:
iOS:
Easiest to use (simplest interface)
Most stable
Far more restrictive
More aesthetically pleasing UI
Better average app quality
Further from the cutting edge of mobile technology
Most pleasing for those who value ease
Most frustrating for those who value customization and/or openness
Far fewer device options
Values integrity of user experience and operating system over user choice
Android:
More difficult/convoluted to use
Less stable, more crashes
Far more open, particularly to developers
Less "polished" or pleasing UI (although ICS is a HUGE step forward here)
Lower average app quality
Much closer to cutting edge of mobile technology
Most frustrating for those who value ease
Most pleasing for those who value customization and/or openness
Far more device options
Values user choice over integrity of user experience and operating system
Obviously, these are simply my impressions from having dealt with each of these over the past few years. Personally, I choose Android every single time, and make a point of never spending money with Apple, as I have serious disagreements with several key tenets of their various company and design philosophies (the link from JimH on the draconian restrictions on revenue drivers that don't directly help Apple over independent developers is a solid example). I do, however, think the marketplace is vastly better as a result of having Apple here-- their focus on the user experience above all other things has really driven the other competitors in the market to do things that would not have been accomplished otherwise. (At one point, I carried a Motorola Q running Windows Mobile-- if ever you wanted definitive proof that mobile operating systems needed a LOT of additional focus on the user experience, look no further. A total trainwreck of an OS IMO.)
As a fan of many subgenres of metal, the progression of Apple in the marketplace reminds me a bit of the hair metal bands in the 80s-- they offered a far more palatable, if generally less musically satisfying, version of metal that opened the door for a LOT of people to get into a form of music they likely would not have encountered otherwise. This can be (and very frequently is) viewed as strongly positive or negative, depending on your personal leanings.
Overall, I think that what I value in a mobile operating system most closely (although not perfectly by any means) aligns with Android. Apple is a completely valid choice for people who appreciate and value their products and business decisions-- I just am not one of them.
Hope this contributes to the conversation!