Quality issue importing illustrator file into after effects

Set the Magnification Ratio in After Effects to 100%. Now you are looking at the pixels in the video. That's as big as the video will be. If your AI file's artboard is 200 X 200 points or pixels and you turn on Pixel Preview, you'll see the same thing you see in After Effects when viewed at 100%.

For artwork that small, you must, and it is an unbreakable rule, have all horizontal and vertical lines precisely lined up with the pixel grid. You should have Snap To Pixel turned on in Illustrator. No horizontal or vertical lines can be smaller than 1 point (pixel). 

200 X 200 is too small to read the small type on the can if you look at pixels. It also looks like you have raster effects like drop shadows on the AI file.

Why so small? This is your image at 200 X 200 pixels.

In your screenshot, the image is almost exactly 800 pixels wide. If the preview in Illustrator was set to Pixel Preview in the view menu and you set the magnification to 400%, it would look just like it does in After Effects. 

This screenshot is 1000 pixels wide in your browser. 

Even by today's standards, 200 X 200 on any device, that's tiny, tiny, tiny. Most displays double up on pixels, so if 200 X 200 on a web page is the final goal, a pixel-based image should be 400 X 400, and the size should be set to 200 X 200 in the HTML code <li-image width="200" height="200" >. That would at least give you the option of having a little sharper image on a high-rez display.