My take on it is, that iPhone users only THINK they use their phone a lot, while Android users use their phones more than they think they do.
Sadly, it's arguably the other way around. The problem isn't that Android users use their phones a lot, it's that the phones (or rather, the OS) is terrible at not using the battery when the user isn't using it. A skilled and conscientious user can regulate their Android phone's battery use pretty well, and get excellent battery life (without compromising functionality much), and there are apps to automate some of that, but... by default, Android is *terrible* about leaving stuff running in the background. This makes it more functional than the competing OSes in some ways, since those tend to have pretty strict restrictions on background processing, but sometimes the stuff it does (like continually tracking your location if you open Maps and then don't tell it to kill the location service when not needed*) is just stupid.
Yes, when you're running something that will really pound on the battery (like gaming) then Android devices might outlast their competition. They do have larger batteries, in most cases, and their processors are no less efficient. The reason for those larger batteries, though, is because in order to get anything close to the same average battery life in normal usage Android needs more battery capacity. Expand the time scale from a few hours of intense usage to a day or normal usage, and Android will usually burn through a lot more Watt-hours for the same level of user usage.
* Caveat: This was something I noticed on my father's Android 4.0 device; they might have fixed it since. It was fucking stupid though; he'd used Maps for a few minutes in the morning (with location, but not navigating to anything), then gone back to the home screen without force-killing the app or turning off GPS, left the phone in his pocket the whole rest of the day, and found its battery nearly dead in the afternoon. Over 90% of the battery had, over half a day, gone into tracking him as he wandered around a boatyard with the app neither running in the foreground nor under orders to do anything in the background!