Could not resist looking at this post 😛 I did some tests to observe the differences.
In the case of AE polar coordinates will always make a circle, the circles diameter seems to be the height of the footage. I observed this by also adding a transform effect before the polar coordinates effect and adjusting first the scale of the height and after the width. The only time it changed the shape was when I adjust the height, internally I am guessing AE is making the image taller in pixels and then polar coordinates picks up that value.
Based on this to solve your problem (as has been suggested) it has to be a post transform-scale to correct it. You would work out the % difference in your image sizes 1280/640 = 2 , scale the width after polar coordinates by this amount 100%* 2 = 200% . I write it here as a formula as you might some day have other sized footage and I am sure this would allow you to add a favorite effect with a small script to automatically scale the image after depending on your original image sizes. (I think the logic here of the simple formula would work if the height was taller than the width…not tested it though). I rather do the transform in the effect panel because it frees my normal timeline transform for animation and I can add scripts to the effect with out effecting any animation I might have already.
Hope this helps and thank you for pointing out the odd quirkiness..next I am off to see how we can make PS act like AE polar-coordinates. As to why they behave differently we can only assume PS stretches the image to the height and width of the canvas just because it felt more artistic, what people might want?? I have not used polar coordinate graphics before in my work so I am not sure what the standard look is seems a circle would make more sense..maybe someone else can chime into there uses I am thinking more used in 3d sphereical mapping but used same manner in AE?
Regards
Chris Forrester
demoreel https://chrisforrester.tv