After Effects always works in pixels; sometimes, you need to look closely at the pixel. Check the bottom left corner of the Composition panel. You have magnified the view to 1600%. Turn on Pixel Preview in Illustrator and magnify the view to 1600%, and you will see the same thing. It's just like Photoshop.
Continuously Rasterize only fixes edge problems when you scale a vector layer or move a camera close to the layer. If you add a raster effect in Illustrator, like a drop shadow, CR will not affect the scaled layer, and you need to keep your scale value to a maximum of 125% if you want crisp edges.