Atomistic quantum transport simulation of realistically large devices is computationally very demanding. The widely used mode space (MS) approach can significantly reduce the numerical cost but good MS basis is usually very hard to obtain for atomistic full-band models. In this work, a robust and parallel algorithm is developed to optimize the MS basis for atomistic nanowires. This enables tight binding non-equilibrium Greens function (NEGF) simulation of nanowire MOSFET with realistic cross section of $rm 10nmtimes10nm$ using a small computer cluster. This approach is applied to compare the performance of InGaAs and Si nanowire nMOSFETs with various channel lengths and cross sections. Simulation results with full-band accuracy indicate that InGaAs nanowire nMOSFETs have no drive current advantage over their Si counterparts for cross sections up to about $rm 10nmtimes10nm$.