The evolution of Gaussian wave packets is theoretically studied under different kinds of governing equations, and the critical asymmetric features of propagating wave packets can be effectively captured by the higher order nonlinear Dysthe model. Moreover, laboratory experiments run in an offshore wave basin are systematically compared with a large set of numerical simulations, respectively performed by using the third-order and fourth-order nonlinear wave models. In comparison with Dysthe simulation, the NLS model presents a more intensive energy focusing, particularly at the intermediate stage of evolution process in the presence of strong nonlinearity. Fitting the statistical distributions with the linear, second-order and third-order statistical models indicates that although bound wave effects also contribute to the deviation from a Gaussian process, it is the modulational instability that primarily determines the discrepancy in the evolution process. Wave crest is more sensitive to the quasi-resonant four-wave interaction effect than wave trough and the scaled maximal wave crest presents a linear regression model with the coefficient of kurtosis. With the increased third-order nonlinear effect the difference between NLS and Dysthe simulations is enlarged and mainly reflected on the distribution of wave crest.