I could run Company of Heroes (I specifically went up to 2GB of RAM to make sure I could, in fall 2006) OK on my sloth system (AMD 64 3200+), but Opposing Fronts initial mission brought it to its knees.
I still am on the first mission in Opposing Fronts. I guess my problem is I really preferred CoH's first few smaller-scale missions that gradually introduce you to units and aren't totally fixated on base building and rushing. I got bogged down when the initial campaign went larger scale and started to feel too much like RTSs in general.
Opposing Fronts' campaign, from what I could see, starts big and massive, and it sort of disappointed me it didn't have something more like the more intimate scale early missions from the original game's campaign.
Still, when I get a new PC (definitely on my New Year's Resolution list, It's been 4 years now), this will be one of my first tests on it.