I'll add that the screen draws significant power too. Combination of screen, CPU + GPU (particularly for intensive web pages) and the (especially cellular) wireless draw a fairly significant amount of power.
I have an old iPhone4 which (even 2 years ago when I actually used it) was struggling to get through a day of light-moderate use. I'm now using it as a second phone for a project I'm on and I've basically turned off 3G and am just using it as a dumb phone. Now that same battery lasts a week easily, I'm making a bunch of phone calls, sending text messages, occasional internet over wifi, etc, but no web browsing and absolutely no 3G... makes the world of difference to battery life.