The temporal and spatial evolutions of nonlinear wave groups with different initial steepness are numerically studied under the governing of MNLS equations. It reveals that due to the slight discrepancy in the dispersion relationship, the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the case with strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical models, are systematically compared with mechanically generated waves with different initial directional spreading and Benjamin–Feir Index (BFI), mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. Although a certain degree of discrepancy is detected, it still can be concluded that the statistical properties of both numerically simulated wave fields are basically consistent with the laboratory observations. The maximal extreme surface elevation tends to appear in the case of long-crested waves rather than in the unidirectional ones. The width of 3D wave spectrum broadens gradually with various degrees depending on the initial BFI, and a small downshift on the peak frequency can be clearly observed.