For example, all things being equal (same nits, GPS on or off on both, etc) the iPhone has similar battery life to the Note 3 on WIFI web browsing. Ars technica confirms this too.
Proof
Your comment just prove that Note 3 technically is superior to iphone 5S. You have to understand that Note 3 is having Full HD 1920x 1080 resolution + 3G ram, and Iphone with much lower resolution , screen size and less ram and only able to do similar battery life as Note 3.
And your comment also prove my point that having more ram would not make the battery life shorter.