SiC was looking good a few years ago -- if still rather expensive -- but then some jerks went and invented the superjunction process.
Right now, SiC is comparable to SJ MOSFETs for 600V+ applications. Neither is relevant at lower voltages (sub 400V or thereabouts), nor are IGBTs. Operating temperature is limited by encapsulation, unless you want to go well out of your way to find the mil spec gold bonded ceramic kind ($$$, lead time
).
SiC schottky diodes are good of course -- if lossy (significant junction resistance) and still on the expensive side.
GaN is pretty cool stuff, but still much too niche-ey for anything but high-falootin' RF. If they ever release HV devices in GaN, it'll be pretty awesome for high [power / frequency / efficiency] inverter/converter applications. Right now, about all that's available are the EPC solder-bump dies, which only go up to 200V. Excellent specs, pricey, probably not easy to solder (fine pitch, but not impossible to manufacture).
Tim