The CAK is in a different class altogether. It is not just a heavy chopper, it is a very big heavy chopper and in no way could it ever be considered a camp/survival kukri. The CAK is a great kukri if you want a dedicated heavy chopper, possibly one of the best but, for the tasks you laid out the BAS will be the winner hands down.
Keep in mind the BAS was designed for soldiers to carry on foot patrols in the jungle and to handle all the chores associated in a camp/combat/survival situation so it should fit your needs perfectly.