The CWC vibe is:
A well written campaign. With memorable missions. (Doesn´t mean humongously complicated). And enough missions to give the campaign actually a feeling of length and depth. Arrowhead has about 10 missions too few. Ditto for Harvest Red. Everything moves too fast, there is no sense of progression, only jumping.
Well. written. campaign.
Many. Missions. Memorable. Missions.
No half-assed, kit-bashed, jury-rigged, barely working features. No undocumented or wrongly documented ingame features or mission components. For example, in the final mission of harvest red, you could get a journal entry for a mission that was removed during development. The entry was left in. It annoyed me so much I stopped playing the campaign then.
Show that BI can deliver AAA titles, not just wah wah wah massive sandbox kits the community can repair.
My two worthless cents on the topic :V
Edit: Also, a fantastic soundtrack. Arma 2s soundtrack was just eh. The only track I remember is the chernarussian anthem. While the OFP theme still comes to me in my dreams, figuratively speaking. Music is -extremely- important.
Also Voice Actors (!). The ones in CWC were, at the time, expensive and rather high-profile types. The ones in the arma series, sadly, have been performing poorly. Not to bash their valiant attempts, but everything was overacted (Especially in Arrowhead), awkward, and the voices didn´t fit the characters (black persons speaking with the voices of middle aged white men? Even as a central european, I found that grating.)
Serious money will need to be invested to fix this. I hope BI has the spare change to adress this.