I redrew the image on the left in Blender, but I want to use AE to achieve the "filmy" look on the right. What type of effect did they use here? You can see from the corner of the screenshot the blue area and the black lines are almost glowing?
Looks to me like a kind of "chromatic aberration" effect - where the red green and blue channels of an image are processed separately - sometimes shifted in position or blurred a little, then they are recombined back together. There are lots of ways to do this using built in plugins, or using 3rd party plugins such as Red Giant's.