Do different species eggshells have different texture? That would be interesting. If so then yes you would be able to distinguish between them. You would need to use a 2D detector to properly and quickly measure the texture. I would assume that the elemental composition would also be different in eggshells of different species. You could perhaps use XRF (x-ray fluorescence) to measure the elemental distribution as a fingerprint for egg shell speciation. Good luck! I would be interested to hear about the results. Please post again once you do some measurements.
I would install a long, thin, sample vertically in the X-ray beam and rotate it slowly while recording the counts with a "banana" detector. If orientation exists, you should see a kind of Gaussian distribution of counts vs angle, and the mosaic spread of the sample will be the FWHM (full with at half maximum) of your distribution.