The energy consumption of purely convective (i.e., various air volume (VAV) mixing ventilation) and combined radiant and convective HVAC systems (chilled ceiling combined with mixing ventilation—CCMV or personalized ventilation—CCPV) was investigated with multi-variant simulations carried out the IDA Indoor Climate and Energy software. We analyzed three different climates: temperate, hot and humid, and hot and dry. Our results show that the use of CCPV substantially reduced energy consumption compared to the conventional VAV system in hot climates. We also show that increasing the room temperature to 28 °C is an effective energy-saving strategy that can reduce consumption by as much as 40%. In the temperate climate, the VAV system was preferable because it used less energy as it benefited from outdoor air free-cooling. The control strategy of the supply temperature of personalized air had an impact on the energy demand of the HVAC system. The most efficient control strategy of the CCPV system was to increase the room temperature and keep the supply air temperature in the range of 20–22 °C. This approach consumed less energy than VAV or CCMV, and also improved the relative humidity in the hot climate.