Do the blades of the rear disk have different geometry to the blades of the front disk on a contra-rotating assembly?
The conditions at the rear disk are obviously different, so something must be different.

First of all, if the rotation direction of the disks is opposite, you'll have 'right' and 'left' blades. (Blades nearly always have asymmetric airfoil, so you can't swap them). That's 'different geometry' already.

Normally, the efficiency of the rear disk will be somewhat lower (zymhan's answer provides some sources). If so, an optimal design should provide more power/torque to the front disk. The most powerful turboprop NK-12 delivers about 20% more torque to the front disk.



Source

This doesn't mean, however, that the blades must be substantially different (other than mirrored). Indeed, on most coaxial assemblies they are the same (including the aforementioned NK-12). How does it work? All these props are constant speed units (at least, I'm not aware of others). The governors will simply set the appropriate blade pitch such that the RPMs were the same, despite different torque and conditions. This means in practice that the blade pitch on the rear disk will be lower. This may count as 'different geometry'.

Finally, there are rare examples when the disks are substantially different. One of them is the SV-27 propfan on Antonov-70, which has even different number of blades (8 vs 6). (This, I believe, is a prop with the highest disk loading ever).



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