CoH is more about tactics, managing small units in a small environment. Very limited base building, as in you have X spot allotted to build on and X, X,X and X buildings you wish to build. You only control ground units, only exception being calling in air strikes as a special ability. Climatically it looks cooler as well.
Supreme Commander is more about balancing base building and creating your army. It is on a HUGE scale with zoom that lets you go from global view of the battlefield to a single unit taking up your entire screen with up to 1000 units per team. You can build land, sea and air units. You can turtle, rush, swarm or out tech your opponent. It is the more traditional RTS.