The Note 2 has a bigger screen but less pixels, s4 a small screen with more pixels. So the video peformance is not very different because the s4 needs more power to manage those extra pixels. And of course personal preference.
Actually the case is not as simple as "1080p is 2.25 times more pixels than 720p"..
Let's count Sub-pixels on Note 2; there are 3 sub-pixel for each pixel thus giving us the number of 3 x 720 x 1280 = 2764800
Let's count sub-pixels on S4; there are one blue sub-pixel for every pixel and there are one red and green sub-pixel for every two! pixels giving us the number 1920 x 1080 = 2073600 blue sub-pixels, 1920 x 1080 x 2(for red+green)/2(for sub-pixel sharing)=2073600.
In total = 2073600+2073600=4147200 sub-pixels.
The expected ratio= 2.25
The real ratio= 4147200/2764800=1.5
Still, the GPU has to push every image rendering for a 1080p calculation. This is why the power is wasted. It calculates everything 2.25 times more than a 720p GPU just to be able to draw it inon a 1.5 times sharper screen.
I am not against a 720p pentile screen because it pushes the 300ppi barrier so it can be more sharper for human eye in certain conditions, however a 1080p pentile screen with a "false/fake" 441ppi is just overkill for both the battery and the GPU..