Quasi two-dimensional perovskites have attracted great attention for applications in light-emitting devices and photovoltaics due to their robustness and tunable highly efficient photoluminescence (PL). However, the mechanism of intrinsic PL in these materials is still not fully understood. In this work, we have analysed the nature of the different emissive states and the impact of temperature on the emissions in quasi two-dimensional methyl ammonium lead bromide perovskite (q-MPB) and cesium lead bromide perovskite (q-CPB). We have used spatially resolved phase-modulated two-photon photoluminescence (2PPL) and temperature-dependent 2PPL to characterize the emissions. Our results show that at room temperature, the PL from q-MPB is due to the recombination of excitons and free carriers while the PL from q-CPB is due to the recombination of excitons only. Temperature-dependent measurements show that in both materials the linewidth broadening is due to the interactions between the excitons and optical phonons at high temperatures. Comparing the characteristics of the emissions in the two systems, we conclude that q-CPB is better suited for light emitting devices. With a further optimization to reduce the impact on the environment, q-CPB-based LEDs could perform as well as OLEDs.