The second equation is more complete as C mineralization can be expressed by g of dry soil but both equation are based on the same principle (Mc/2= 12/2= 6 (eq 7.1) and E=6 in the first one, NE= 0.05E=0.05x12/2 if C-CO2)
Second equation seems to be more appropriate. Brigitte Brunel, very clearly pointed out that both the equation based on same principle. However this is good topic to study.