Concrete as a cutting surface
It's pretty much common sense that your wouldn't want to cut directly on the concrete surface. There are few surfaces you would want to. Forget the potntial damage to the countertop surface for a moment. Doing so would make your knives dull...
Many of the concrete countertops I've seen have recesses molded into them to hold cutting boards or serve as drainage areas for dishes. This sort of thing is not easily accomplished in other materials except solid surface material (Corian, Avonite and others) where it can be done during fabrication. I plan to build a removable cutting board into my countertop right next to a sink with a garbage disposal installed. This way, when doing food prep the waste can be pushed right into the sink. The other approach would be to create an opening in the surface with a can beneath to catch the waste.
IMO, there isn't a better cutting surface than hard maple. The board can be removed for cleaning. When it becomes unsightly, I can just make a replacement. There has been some disagreement about sanitation when using wood cutting surfaces. If this is of concern to you, a UHMW plastic cutting surface could be substituted but I don't think it would look nearly as nice as maple.