Since you asked for what advantages iOS offers other than the general look and feel of the OS itself, here goes:
1. iOS is much, much better for gaming. Since I like games, and spend a lot of my free time playing games, I like having OS and hardware that's good for gaming. That's part of why I actually won't buy a Mac any time soon. And also exactly why I like iOS. It's far superior to both Windows phone and Android in gaming, with far more exclusives than either. The only exception to that rule is the NVidia Shield, which is a better gaming device IF you have a good PC to stream all your best games from. Which sadly, I do not. So iOS it is, for me.
2. Security. Unfortunately, I don't think Google will ever catch up in this area, partly due to the fact that their OS is open unlike iOS, and partly because the thing most of us want security against, apps that track you and sell your info, is Google's biggest revenue source. Either way, this advantage should be fairly evident to anyone who knows about the OS. iOS is sandboxes so malware cannot spread itself throughout the OS, and it lets you micromanage what each individual app is allowed to access on your phone.
3. The App Store is far superior to Google Play in many ways. Sure, Google. Play wins out in a few areas, like customization apps, replacing defaults, and possibly in apps that Apple refuses to support, like emulators and the like. However the App Store quite simply has a far larger selection of apps and several exclusives (the first one I can think of is Facebook Paper).
4. Integration. Between all the integration already introduced, and the more that's coming in iOS 8, if you already have an iPad or Mac, you have plenty of reason to want an iPhone, and vice versa. The fact that a lot of this integration is available in some limited capacity for Windows-iOS too, helps.
5. Android's biggest advantage, customizability, is rendered moot by a 5-minute process. I simply cannot stress this last one enough. Jailbreaking (or Rooting for that matter) offer virtually unlimited customizability. Light years ahead of stock Android and iOS. The thing is, the above listed iOS advantages are nearly insurmountable. Sure you can get a third party solution for security, but those systems always lack something. For example, Google discontinued App Ops because it caused instability in apps. Do third parties take care of that? And the App Store advantage is simply too big a factor to ignore, and can be solved by no one but Google and the Android App Devs. Google is trying to improve integration the same way too, and so is Windows Phone for that matter, but iOS 8 has some killer features that the others don't.
So there are my reasons as to why I would choose an iOS device even if someone offered me a very similar Android device for half the price. That sure is incentive enough for me.