Newer phones not much better
A few weeks ago, for kicks I put my nexus 4 and evo 4g lte on the shelf and started using my ancient Evo 3d again.
To my surprise, I hardly notice I'm using an old phone. Everything runs pretty well,
battery oddly seems longer on the 3d (extended 1900mah vs the N4 anyhow, maybe smaller screen and resolution contributes to this?)
and the 3d is still a fun and even rarer option now.
On the other side, the browser on the newer phones handle large sites better,
and some apps/games may have a little longer load time.. (but they run the same once loaded)
So overall, I'm kind of digging the old 3d more than newer ones.. (albeit not the newest ones, I dont have an S4-era phone)
Re: Newer phones not much better
I think you are partly right on the screen. I think the hardware is pretty close to the same, which is why you are seeing similarities in performance.