The purpose is strictly for those who want to use .40 S&W over .44 spl for some reason. Reasons I can think of are as BUG paired with a .40 S&W semi-auto, for those who want a big bore revolver and don't reload .40 S&W is cheaper than .44 spl, or for people who already do reload .40 and don't want to add another caliber. I have no use for it for either of these three reasons, except I don't reload but want to start reloading in the near future anyways so it's a moot point to me.
I've been wondering for a while now why Charter didn't start with the 9mm or 45acp since both calibers are common and have demand. Maybe it's because nobody at the time was offering a .40 revolver, but it seems to me that there is a bit more demand for the 9mm and .45 versions.
Also, anybody thinking about buying this as carry revolver should look up and watch some of the videos about reloading it on youtube. Apparently, each round must be manually pushed into the cylinder to catch the retention spring inside the star (the part that makes it not need moonclips). This makes it so you can't really use speedloaders, and might slow down speed strips or loading one-by-one a little bit.
Don't get me wrong, I DO think these revolvers have a purpose and I do like Charter Arms, but I just find myself less and less interested in the Pitbull and more and more interested in the Bulldogs: proven design in a proven caliber for that design, slightly longer barrel, and cheaper than the pitbulls plus more options to boot.
Again, the purpose is more for those that want to use .40 because of price or ammo consolidation (same caliber for multiple handguns) than it is for trying to get more power or reliability over the regular .44 Bulldog.
Edit to add:
Great review Mr.Revolverguy! very informative.