We use the local-density approximation (LDA) and LDA+U schemes to study the magnetism of (GaMn)As and (GaMn)N for a number of Mn concentrations and varying number of holes. We show that for both systems and both calculational schemes the presence of holes is crucial for establishing ferromagnetism. For both systems, the introduction of U increases delocalization of the holes and, simultaneously, decreases the p-d interaction. Since these two trends exert opposite influences on the Mn-Mn exchange interaction the character of the variation of the Curie temperature T_C cannot be predicted without direct calculation. We show that the varation of T_C is different for two systems. For low Mn concentrations we obtain the tendency to increasing T_C in the case of (GaMn)N whereas an opposite tendency for decreasing T_C is obtained for (GaMn)As. We reveal the origin of this difference by inspecting the properties of the densities of states and holes for both systems. The main body of calculations is performed within a supercell approach. The Curie temperatures calculated within the coherent-potential approximation to atomic disorder are reported for comparison. Both approaches give similar qualitative behavior. The results of calculations are related to experimental data.