Hm. AE does not reduce quality per se. If you choose to render with a low-quality codec, then quality goes down.
Are you viewing the comp window at full res?
Fine lines will mess up in any app if they are smaller than one pixel wide, as you know. Try applying a 1-pixel (or less) blur in an adjustment layer over the shrunken footage. If you can’t use an adj layer, apply the blur to the footage, but increase the blur to account for the shrinkage.
In what did you view the files before AE, when you saw them as high quality?
What codec are the AVI files?
What do you mean by losing quality, specifically?
Where do you see the quality loss? The Avid? AE comp window?