Look at the design in Figure 2 . Two 3-digit binary numbers can be compared by first comparing their most significant bits. If they are not equal, the result of the comparison will be the final result. If MSBs are equal, the result will be based on the comparison of the second bits. If they are equal too, the result will be based on the comparison of LSBs.
NXOR gates aim to pass the result of the next bit pair if the pair in the current stage are equal.