Background: In heavy-ion collisions at intermediate energies the production of light charged particles and intermediate mass fragments (IMFs) is due to different reaction mechanisms and different time scales, ranging from fast dynamical processes to statistical emission from the equilibrated system. Purpose: We compare the IMF statistical and dynamical emission probabilities in collisions of a neutron-rich ^{124}Sn + ^{64}Ni system and a neutron-poor ^{112}Sn + ^{58}Ni system at the laboratory energy of 35 A MeV. Method: The IMFs production mechanism in semiperipheral reactions has been investigated in our previous works. In this paper, the analysis is expanded for the same set of data and production cross sections have been evaluated for dynamical and statistical emission in a coherent way for light and heavy fragments. Results: The data analysis has evidenced a strong competition between dynamical and statistical emission mechanisms. Probability of the dynamical emission of IMFs is strongly influenced by the (N/Z) ratio of the colliding system. Conclusions: It is demonstrated that the statistical emission is equally probable for the two systems, while the dynamical emission is enhanced for the neutron-rich system, especially for heavy fragments (Z≥6). The observed effect points at a high sensitivity of the prompt-dynamical emission to the (N/Z) ratio of a given system.