I have had the pleasure of owning both a Kangal that I imported from a shepherd in the Sivas region of Turkey and currently two CAO.  I do not know that I can make any accurate assumptions regarding breed temperament differences, as I have observed a rather wide range in temperament within the breeds.  For instance my male CAO (intact) exhibits a higher defense drive against strange human males on property, more accepting of woman and children. Off property he is good with everyone.   My female (intact) is more accepting of humans, is more alpha than the male, has a short trigger with dogs, especially females, and will not tolerate any male dog so much as glance at her in a "challenging manner" on or off property, and is a nocturnal barker (not so good for the neighbors).   Neither COA wonders or ever attempts to undermine my fence.  The Kangal also displayed a territorial protective and defense drive, with slightly less hostility to men than my male COA.  The male Kangal that I owned was more alpha than the current male COA that I own.  Of the three specimen that I have owned (2 COA, 1 Kangal), the female is the most dog aggressive.  None are/were aggressive to humans off property (the Kangal has unfortunately passed).  I have however, observed other Kangal and COA displaying a rather wide variety of temperament behaviors with much cross-over between breeds.  Perhaps the Kangal as a breed may be a bit more social than the COA and amenable to obedience commands on a consistent basis.  I also owned Great Pyrenees in the past, and prefer the Kangal and COA.  Both male Kangal and COA that I owned tended not to consider small to medium sized dogs a threat or challenge and would not respond to even an aggressive confrontation by dogs say the size of a pitbull.  When the dogs were of greater size, or with cropped ears they would assess the risk and respond to the other dogs aggression.