The battle of the fanboys will never end. You could argue the minutiae of where one platform triumphs over the other all day but for any relatively unbiased user, both have reached an experience parity. They are both perfectly capable systems for standard usage.
I used an iPhone 5 for about seven months last year and have been using a Nexus 4 after that. I felt noticeable differences in my mobile habits on both. First and foremost, the camera. The iPhone's camera is better at taking instant shots, perfect for that fleeting moment you want to capture. Sure, the Nexus can take decent photos but they require patience and time, the latter of which I rarely have. You have to hope that the Nexus got the exposure and focus right in your quick snap but it generally doesn't while the iPhone does. Thanks to the quality+speed of the camera, I found myself using Camera+ and Instagram a lot more. Since I actually got good pictures, I would also post them on Flickr after editing them with Camera+ (and even Snapseed). For the Nexus, no photo app comes close to the blend of speed, functionality and UX pleasure that Camera+ offers, so my attempts at photography consequentially decrease in frequency.
Next up is Twitter. If someone were to plot my tweets in a graph, there would be a considerable spike in the months where I used the iPhone. Most of the credit for that would go to Tapbot's masterpiece, Tweetbot. Every little animation and sound effect it has are similar to the little bits of perfection I expect from Apple or Google (Now). Another spike would be in my journaling habits. I write for fun sometimes, about trips, events I went to, books I read, for this blog and Day One is the beautiful app which helps me do that. I know the makers were looking for an Android dev, so there will be an Android version someday but until it is, Day One is another thing drawing me to Apple's ecosystem.
Lock screen notifications are better on iOS because the whole screen lights up with your alert and you can jump straight into the notifying app. Plus, Apple has a patent for this so fat chance of seeing this anywhere else. Beyond the lock screen though, Android wins hands down. The quick-actions and expandability within the notification shade are cool but it's the icons in the notification bar are the important bit. They are a cognitive reminder of stuff awaiting your attention. I can imagine Apple's design team deciding against a host of icons cluttering up the top of their pretty OS but a single "notifications waiting" icon would have done wonders. Maybe even a springboard-zoom-out effect where the notification goes into that icon after popping up. Otherwise, if you miss the notification when it shows up initially, you have no way of knowing what's pending without actually swiping down.
The majority of my computer usage involves being online and the dominance of Google's web services online is unparalleled. Built from the ground up to ensure that mobile users have first-class access to Google products, Android apps are well-integrated into their ecosystem. Google Now is the icing-on-the-cake, the cherry on the pastry, the breeze on a sunny day, whatever floats your boat. It unifies all the data Google has on you, analyses it to predict which information you need and presents it in a gorgeous cardified (Is that a word?) format. Under Larry Page, Google has also stepped up their iOS apps which, while not as tightly integrated due to iOS's restrictions, still offer a great experience for their customers on the rival platform.
Being a human who likes to talk to people, messaging is another big one for me, particularly chat heads. I absolutely love having them accessible everywhere in Android. The floating heads are one possible solution to multitasking on mobile platforms but that problem awaits it's solution on either OS. However, they are severely handicapped on iOS thanks to how guarded the OS is and the lack of proper inter-app communication . Until Apple allows it's developers that advantage, Android's Intents will have the upper hand in allowing the user to choose their app preferences. The iOS keyboard (though very accurate) feels glacial after getting used to one-handed swiping on Jelly Bean. I am sure the folks at Cupertino are experimenting with their own implementation but until they release it, El Goog wins this one. It's need will be felt a lot more if the iPhone 6 rumors of a larger display screen turn out to be true. They have already solved the unreachable top-left corner by using the screen-edge swipe to navigate backwards in iOS 7.
The last one is the filesystem. While I don't think it's required for all users to have access to a file browser, it's a must for powerusers. The developers, tinkerers and enthusiasts (like me) would love a 'dev mode' in iOS. Android is very enabling by letting me use the storage in whichever way I want.
My conclusion? If you need a smartphone, the iPhone is your best bet but if you want a computer in your pocket, then get a Nexus. I might switch back to iOS later this year for a couple of reasons. One, I am not satisfied with the camera or battery life of the Nexus and two, I am an iOS developer so owning an iPhone would make my life a lot easier. So, if you judge these phones objectively, they are both good but based on your usage style, you will gravitate towards one or the other.