Android lets me do what I want with my phone. Apple does not.
If I want to install a custom keyboard, I do. Not just Swype, which is a huge plus for Android & is impossible to add to Apple because of their restrictive OS, but perhaps I want another keyboard with different spacing, or one that doesn't have a voice command button hogging real estate, since I never use it anyway.
If I want to view flash videos or content, I can. I'm not a child, I can decide to risk a page that doesn't load properly. It beats the heck out of a page or video that won't load at all because Apple doesn't want to risk an unstable browser... or has a spat with the software company that kept them afloat (Adobe).
The browser rarely crashes, and flash content doesn't have to load automatically. I have it set to never load, but give me an option with an arrow box. If I want to load that flash ad, I do. If I want to load that full HD video of Battlefield 3, I do. If I want to see if my phone can mildly handle a flash based menu navigation page, I do. I want control and options. I don't want half of the internet.
If I want to add custom widgets to my desktop, I can, like a scrolling google calendar schedule, a set of power toggles (to click wifi, gps, bluetooth on/off with one click), a twitter feed, a small weather app... I can do that. I hit the home screen and swipe right to it, never opening the app unless I need a lot of info.
If I want to change my operating system to something made by smart but random programmers on XDA, I do. I can add a totally fresh, faster, unique and more functional operating system. I am an adult. I can assume the risks of doing so. Technically speaking Google doesn't support this, but both they and Amazon have been pretty lax about it, while Apple has always taken a hardline stance against it. Of course, a few years later, they add many of the features those jailbreaking deviants were adding & using on their phones. You know, like copy & pasting.
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The apple hardware is phenomenal. The camera really is quite good, while most android cameras are either adequate or mediocre... albeit with full HD and high resolutions. Those things are only important if you have the image quality & clarity to begin with. That's where great glass & sensors make all the difference. This isn't to say android cameras stink, they just feel like phone cameras. The iphone feels like an entry level point and shoot (albeit with a limited zoom).
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Apple is the creation of a brilliant, stubborn artist. What it does well is fantastic, and many things are outstanding. What it doesn't do it not only doesn't support but it either fights tooth and nail before supporting, or just puts off for years before adding.
Copy & paste took years to be added to the iphone. Functionality that was decades old.
Same with notifications, which they eventually copied heavily from Android. For a painful number of years, they interrupted everything with a pop up window. For such a great innovator, Apple sure had a prehistoric alert system.
Same with custom wallpapers, another thing you had to void your warranty to add before.
Battery life is far better on Apple. Android has mediocre to lousy battery life with most phones. But there's a catch, like many things with the iphone, where they protect efficiency at the expense of choice. You can't replace the iphone battery. so if you're a heavy user, need to use it out in the cold for extended periods, want to watch outrageous amounts of videos on a series of flights, or might not be able to plug in for days (while regularly using it)... you're screwed. If you're on android, you simply swap in your spare battery, or three. They're dirt cheap.
Fragmentation is a lot less of an issue now than it used to be. In the past, most phone makers tried to add their own stylized "enhancements" to android, most of which just cluttered it up, and were things that people could add to their phones if they wanted, but rarely did. These days more and more phones are shipping with stock android or close to it. HTC still has their own style, but unlike Motorola, their refinements are enjoyable and often mimicked by third party add on apps in the market.
Both markets have tons of apps and most of the same apps. The iphone has a lot more exclusive apps because it has a more developed ecosystem and is easier to program for. On top of phone fragmentation, a new issue is that android tablets often struggle with certain apps that work flawlessly on all android phones.
This is changing, as Android has gone screaming past Apple recently in raw numbers. Both will continue to be great, great markets, but the sheer volume has changed what was a pretty one sided fight (albeit one with enough copycats to prevent it from being painful on Android's end).
There are more free, ad based apps in the android app market.
The other huge thing is the Amazon App Store, which gives away a good app every day for free. Now they've already gone through many of the good titles, but they periodically give away a good one every week or two. Before, they literally went down the list of the best apps and gave one away for free every day.
Third party hardware is infinitely better for the iphone. So many creators can make alarm clocks or stereo docks for one device. No android unit will be relevant in three years. The iphone connector still uses the same connection, even if you have to buy a new case (of which there are also infinitely more than android).
This is a pretty solid summary:
http://www.pcworld.com/article/242139/apples_ios_5_vs_googles_android_40_ice_cream_sandwich.html
