CoH is more along the lines of DoW not C+C as there is no real "harvesting" of resources. but they are similair in the way that a RTS is to another RTS (building bases, upgrades, a few defence structures. you gain resources by capturing points which increase the amount of "supplies" you get given from the invisible high command... ie if you capture a few points the "command" will think its worth investing in your army and give you more points. however it really is just "more points, the more resources"
CoH has a more versatile terrain which actually matters and is highly physical (ie destructable)
and men are often in squads not individual units, personally i find the AI and spacing and terrain awareness pretty awesome. im a big fan and the MP games are sweet.
there is also slight personalisation within the army on what doctrine you choose (3 for each side each with their own advantages)