As two exemplary candidates of wide-bandgap devices, SiC MOSFETs and GaN HEMTs are regarded as successors of Si devices in medium-to-high-voltage (>1200 V) and low-voltage (<;650 V) domains, respectively, thanks to their excellent switching performance and thermal capability. With the introduction of 650 V SiC MOSFETs and GaN HEMTs, the two technologies are in direct competition in <;650 V domains, such as Level 2 battery chargers for electric vehicles (EVs). This study applies 650 V SiC and GaN to two 240 VAC/7.2 kW EV battery chargers, respectively, aiming to provide a head-to-head comparison of these two devices in terms of overall efficiency, power density, thermal performance, and cost. The charger essentially is an indirect matrix converter with a dual-active-bridge stage handling the power factor correction and power delivery simultaneously. These two chargers utilise the same control strategy, varying the phase-shift and switching frequency to cover the wide input range (80-260 VAC) and wide output range (200 V-450 VDC). Experimental results indicated that at the same efficiency level, the GaN charger is smaller, more efficient and cheaper, while the SiC charger has a better thermal performance.