Between my sisters house on 2 miles of dirt road and one of my daughters on a long dirt hill drive I have enough time off asphalt to get a feel for the CT on dirt. If it is a heavily rutted road the rear will still wiggle and follow the rut. A MT will drop into narrow ruts that a wider CT may roll over and not slide into BUT the wider contact patch of the CT will bump steer the rear end as it rolls into a rut so just like any bike with any tire on a loose surface, stay on the throttle slightly to always keep the bike pushing forward.
I will say going down my daughters drive I get much less rear wheel slide and a bit more traction going up.