if you look again at those videos, you'll see that when the user click on some link, or enter address in location bar, the browser just react faster, it start fetching and loading the page almost immediately, while on amiga if doing the same, netsurf seems to wait a while doing nothing before it finally decide to do something.
I don't see any delay here? There was a bug I fixed which might have caused some pausing, maybe you're not using the latest version?
here i'm just guessing, but, i think atari too have to be using sdl for their netsurf port.
It has various font engines, but the plotters are native, not SDL.
I suggest you check the latest Atari build with the latest OS3 one, on similar hardware personally, rather than through a five year old video. It's then possible to determine whether any aspects are faster or slower and investigate why that might be.