ok, try this, from a full charge, disconnect at 6:30am, watch streaming, non-wifi video until 8:00am, then play 30mins of a game such as real racing 3 (3D high processor usage), now, from 9am to the end of the day at 19:30 when you can re-dock, use another 2hrs of streaming video over the air, make at least 5 30 mins long calls, send 25 texts and 10 emails, Spend around 30mins reading emails and spend a further 45mins googling technical information for various server related issues,
without charging at 19:30, Blutooth off, GPS on "automatic", wifi on, screen brightness set to 40%ish
my Samsung Galaxy S2 lasts me around 21hrs at this usage level, the iPhone 5, dead by 11am, if i was lucky to get that far,
Add to that the Frustration that having to carry a non-standard cable around, or an adapter so i can use a micro usb to charge and its just too much hassle, so i carry an iPad mini, which DOES last all day (around 40% charge by the time i get home) and use an android phone, that, you know, just works...