From: Montreal, Quebec
HI jpc, welcome on. I too own all 3 CM games, and I recently bought the CS edition. Here's the beef. While CM has more micro-management. ( you move individual squads/vehicles ) CS takes this concept up a notch, by allowing you to move platoons/gun sections instead. You don't get to destroy individual buildings, but rather you could rubble generic villages /towns. You select ( in the dynamic campaign mode) the level of your command ( battalion/regimental, divisional), but it all remains at platoon level. ( in the linked campaign mode, leaders are individual counters)
You still have to deal with supply rules ( as such, out of ammo, out of touch with HQ,etc..) so you can't go haywire with your units without suffering some form of penalty. Finally, you have air cover, AA rules, hundreds of AFVs with their variants, scenarios galore, GREAT mod created scenarios as well, plus your usual pbem, online, etc..The AI can be tricky too, at times.
I hope this brief overview helps you. REply if you got other questions.
"Si Vis Pacem, Para Bellum" - Publius Renatus, 390 A.D.