GaN Vs SiC physic properties
As there seem to be no other answers, I undelete mine. While I think, it doesn't answer your core question, maybe it will stimulate someone to provide that. :-)
SiC and GaN address different sectors. GaN is an often superior replacement for Si superjunction MOSFETs in the ~600V segments (mains switchers / rectifiers). SiC is best for higher utility voltages that GaN can't (yet?) address. I believe SiC excells at very high powers due to its thermal properties, such as locomotive and replaces IGBTs and to some extent tyristors.
SiC are MOSFET or JFET with SiC instead of Si. These transistors are rather similar to traditional Si, but with better properties in many respects, such as lower gate capacitance for the same power (why?) allowing higher frequency or higher efficiency, possibility for higher breakdown voltage (due to wider bandgap) and lower reverse recovery parasitic for diodes (why?). Maybe some of it is related to the fact that some SiC MOSFET are actually smaller Si MOSFET steering SiC JFET.
GaN transistors are substantially different, being usually HEMTs and not MOSFETs. Nevertheless they are controlled with a gate voltage. Their gate charge is very low for the same power allowing very high frequencies while still offering rather high breakdown voltages, albeit not as high as SiC. They also conduct in reverse, mimicking the body diode aspect of traditional 3-terminal MOSFET, but have no reverse recovery, as the reverse and forward conduction path are identical.

Graphics like this show that the theoretical figure of merit is better for SiC than for Si, and better yet for GaN. But I don't know how this is calculated. And this also skips over other important metrics, such as reverse recovery and gate charge properties. This graphic seems to indicate that especially GaN is still far from mature.