You have not provided any proper details about your project settings, comp settings, render settings, your version of AE, system info, how you prepare your artwork and a gigazillion otehr things. Simply saying that it doesn't work is not good enough. From your screenshot the only think noticeable is the different resolution and inevitably that will affect rasterization of vector artwork.
There's not enough information to tell exactly what is going on but I'm guessing that you either did not move all attributes to the pre-comp or that you are nesting a comp that is a different size. Your timelines do not show us any properties (select the problem layer and press the U key twice to show every changed property) and your source footage and comps are not selected in the Project Panel so we don't have any idea what the comp or footage properties are.
Your composition sizes don't appear to match. HD for one, and a custom 960 X 560 for the other. The problem is workflow.
If you imported the Illustrator files as a composition then go back into AI and set the art board to 1920 X 1080 pixels then re-import as a comp.
If you actually pre-composed the layer in question (it doesn't show that in your screenshots) then you must select Move All Attributes to the new comp and the Pre-comp will be the same size as your original. Otherwise, only the layer will be pre-composed and you'll loose anything you did to the layer in the main comp before pre-composing.