Vector comes in pixelated no matter what I do_Illustrator vs After Effects

Ok, so we've eliminated Continuous Rasterization and resolution. If your magnification setting isn't the issue, we'll start exploring other things.

Do you have any effects on any of these layers? We can't see your top layers - is there an adjustment layer up there, perhaps?

So here's your screenshot:

Which by its self is almost completely useless in diagnosing the problem. The clue is that I can see the actual pixel grid. That tells me that the Magnification factor is probably 800%. It might be 400%.  The Comp Panel display is always pixels, never vectors. If the Magnification ratio is 100% or 200% for HR or Retina displays, and you scale a vector image up 2000% and have Continuously rasterize turned on it will always look sharp. With CR turned off it will look aliased. My experienced eye can tell the difference between Aliased and just looking at pixels. Check the corner of the comp Panel. Here's a shape layer, which is always vectors @ 1600% and the view is perfectly normal.

Are you enabling Continuous Rasterization on the layer(s) in question?