Google services- Easily accessible through the browser as opposed to being limited to a brand of hardware.
Google Now- I have this widget on my lock screen and I can't tell you how much this helps me keep my work day organized. Not to mention, auto recommendations based off location for either recreation or business.
I have a set configuration that works for me which consists only of a launcher and keyboard. I don't tinker anymore.
Better suited, at least for me for both productivity and media consumption due to expandable memory (either via OTG or SD card support) with quicker file downloads.
I find the UI of Google apps and those that follow the guidelines incredibly intuitive.
Inter-app communication/sharing.
I find the notification to be more seamless (touchwiz, the only thing they got right). A one stop shop so to speak.
I find that the overall OS design enables greater use of screen real estate.
I currently own a Note 3 and find it to be the most responsive, well rounded phone I've used (with Nova Launcher Prime).
----------
I love being able to set default apps, it immensely annoyed me receiving a link in anything, Facebook Chat, Text, Email etc and having Safari open it without my consent.
I like being able to download files in the Web Browser etc. I love having access to the file system, I do often use it. I love being able to drag a .mp3 into my "ringtones" or "Notifications" folder to be able to use it.
I dislike having my entire homescreen cluttered with icons, I do use Widgets, I love being able to change icons and stuff.
Those are my personal reasons for preferring Android over iOS.
Heh, I completely forgot about this and take it for granted. Forgot I couldn't do this with my other devices.