I guess the results should be identical, because they work the same way. Just that one's natural and disposable while the other is artificial and rechargable. You can actually see the Purigen is working because it slowly goes dark brown as it becomes saturated. With charcoal, it's impossible to tell fresh from old!
In theory, Purigen should last forever with infinite recharging. It's a lot more expensive than an equivalent amount of charcoal, but the costs work out about even over a 12 month period.
So it's pretty much 6 of one and half a dozen of the other, performance and cost-wise over a year. For lazy people like me though, disposable charcoal is the way to go considering the hassle I went through of recharging the Purigen!

(PS. Disregard that thread of mine you linked to. The problem turned out to be an increase in chloramines in my tap water, not the Purigen leeching bleach as I first believed.)