Matrix behavior is expected to widely influence the impact response of composites, but detailed conclusions in the case of thermoplastic laminates are still needed. In this paper, we investigated the effect of using either ductile homopolymer PP or less-ductile impact copolymer PP matrices on the low-velocity impact responses of continuous glass fiber-reinforced polypropylene (PP) laminate. These PP types represent two variants in the same family of thermoplastic matrix. A thorough experimental campaign was first performed to provide the tensile properties (for PP and glass/PP) and fracture toughness (Mode-I and Mode-II, glass/PP only) of the employed materials. Then, low-velocity impact tests where the energy levels are ranging from 12 to 30 J were performed. Using ductile PP in glass/PP laminates reduces the energy dissipated during impact as well as the impact damage area. The effect of selected stacking sequences on the resistance to impact was also studied as a way to reveal the difference between ductile and less-ductile glass/PP. Stacking sequence with thin plies shows better impact properties than other sequences regardless of the matrix ductility, which can be explained by micromechanics for both grades of material. Finally, as quasi-static indentation (QSI) is usually used to quickly access the resistance of laminates towards out-of-plane impact, we systematically compared our impact results with QSI results. We found that the prospective use of QSI in forecasting impact properties and damage is very limited in glass/PP composite due to strain-rate sensitivity.