Conical nozzle flows are studied for Reynolds numbers of 1,230 and 12,300 using different numerical techniques: DSMC Method, Navier-Stokes with velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of the BGK and ES-BGK equations. Detailed comparison of the accuracy and convergence of the employed numerical techniques provides better understanding of their benefits and deficiencies, and assists in selecting the most appropriate technique for a particular nozzle flow application and available computational resources. The deterministic and statistical solutions of the BGK equation were found to be in good agreement with the benchmark DSMC results. The Navier-Stokes solution was found to differ from DSMC in the boundary layer. Statistical BGK and ES-BGK methods are shown to be more efficient methods than DSMC in the continuum and near-continuum regime, and more accurate than the solution of the Navier-Stokes equations in the transition regime.