The odd-even staggering of the yield of final reaction products has been studied as a function of proton (Z) and neutron (N) numbers for the collisions ^{84}Kr+^{112}Sn and ^{84}Kr+^{124}Sn at 35 MeV/nucleon in a wide range of elements \left ( up to Z≈ 20 \right ). The experimental data show that staggering effects rapidly decrease with increasing size of the fragments. Moreover the staggering in N is definitely larger than the one in Z. Similar general features are qualitatively reproduced by the _{GEMINI} code. Concerning the comparison of the two systems, the staggering in N is in general rather similar, being slightly larger only for the lightest fragments produced in the n-rich system. In contrast the staggering in Z, although smaller than that in N, is sizably larger for the n-poor system with respect to the n-rich one.