Does After Effects run faster with .ai or .psd or rasterized files?

Dave is right. Complex vector images can take a long time to decode, longer than the same frame size in a raster image like a Photoshop file. On the other hand, a simple solid color as a Photoshop file will take less time to decode than an image with a lot of colors and detail. The fastest rendering image file depends entirely on the image and what is going on. All things being equal a vector file that is as complex as a photograph, something like this:

From Adobe Stock would probably take longer to render than a similar properly sized photograph.

The more important question is what do I want to do with the image. If you plan on doing big moves, then vector files are almost always preferable.

Thanks, but I guess I don’t understand what you’re saying. Let‘s say all things being equal, as in I’m just trying to change the position, scale, rotation, etc. of a layer… What type of layer is going to move faster and smoother, and allow me to preview at full resolution the fastest?