Probably the least relevant benefit of APNG over GIF: Unlike GIF, I can even pronounce APNG with a soft G and not feel gross about it. (Like I’m betraying the peanut butter brand and my entire moral framework at the same time, y’know?)
Strictly-speaking, last time I took a serious look at this, which was quite some years back, it was possible to make very small GIFs that were smaller than very small PNGs.
That used to be more significant back when "web bugs" -- one-pixel, transparent images -- were a popular mechanism to try to track users. I don't know if that's still a popular tactic these days.