I dont know what koa sounds like - I've read generalisations, but never played one, let alone enough to make a composite understanding from experience.
But as a rule, the CS is lower output, less compressed, more organic, less bassy and middy, brighter. Reverse for the PK and add that its got a really strong pick attack in the upper mids, as jonathan says, thats very popular for 'djent'. I personally find that same thing a bit clicky sounding.
Overall the PK is the best bet, likely regardless of woods. I'd only go for the CS for generic djenty sounds if you were tuning VERY low (like G or something) and were using dark sounding woods.