i dont quite understand what are you trying to achieve but you could use transform feedback (draw first the white shape) then blue shape on top of it (you compare pixels and output the data via tfb) then process results on cpu

Interesting idea you have there, the image you posted looks appealing too, I like the style.

If I understand this correctly you should draw both textures (the user's and your own) onto another frame buffer/texture by combining them using XOR. You could do this using the alpha channel of the texture assuming the alpha is either 0 or 1 using a simple shader. If the values of the textures are different (one is 1, the other 0 or vice-versa) then you color the pixel on your 'checking' texture that you are creating otherwise you leave it black. That should then give you a sort of error mask with the parts that are different/wrong being colored in. You just have to count up the pixels that are colored and that should give you an error value (0 would be perfect) but how far off they are will depend on the size and resolution of your texture.

In the above image you would end up with a big black texture with the blue part being white except for where the blue and the white inner shape overlap (that would also be black).