When ice grows, the growth rates are equal along different growth directions and some layers contain planar defective regions. With the aim of helping to understand these phenomena, we report the molecular dynamics simulations of ice growth on the basal and prismatic faces of initial hexagonal ice, using the TIP5P-E water model. By presenting the time evolution of the two-dimensional density profiles of water molecules in each layer and the kinetics of layer formation during ice growth at the temperature of 11 K supercooling, we show that two forms of ice arrangements, hexagonal and cubic, develop competitively within the same ice layer on the basal face, whereas such in-layer stacking-competition is insignificant on the prismatic face. It is shown that, on the basal face, the occurrence of significant in-layer stacking competition in one of the layers significantly delays the layer formation in several overlying layers and explains the overall delay in ice growth on the basal face compared to that on the prismatic face. In addition, it is observed that large planar defects form on the basal face, as a consequence of the long-lasting in-layer stacking competition when the overlying layer grows rapidly.