To add to Mike's detailed post above, there's also the consideration of ease for the user/owner to touch up the edges on the different types of grinds.
As Mike mentioned, a Scandi/Scandinavian grind is easy to touch up, due to not having a secondary bevel. You just lay the blade on the whetstone. Sharpening one/touching up the edge is pretty similar to doing so with a chisel.
The downside is that the edge is less durable than other grind types. Good for things like carving wood, or slicing, but more fragile for chopping and you don't want to use a Scandi grind for batoning. Off angle/lateral forces can warp the edge of a Scandi grind more easily than the others.
A convex grind is more forgiving to lateral forces (bad chop angle, or splitting/batoning wood with wavy grain), due to having more meat behind the edge, and the lack of a shoulder between a primary and secondary bevel, can reduce drag in the material being cut/chopped (although as Mike mentioned, not all convex grinds are equal), but there are downsides as well.
A lot of folks have trouble cutting anything in a somewhat straight line, with a convex grind. A flat grind, or flat(ish) primary bevel sort of acts as a plane that keeps the blade straight(ish). The curve on convex grinds requires the user to do so.
The other downside is that many folks are used to sharpening edges with either a secondary bevel, or a Scandi/flat grind.
Sharpening a convex grind requires different methods. I know of more than one person who's bought a convex grind knife, and wound up putting a secondary bevel on it the first time they needed to sharpen it, simply because that's what they're used to, and what's easiest for them.
CPK knives have a primary and secondary bevel. When done properly (as any CPK owner can attest), there is minimal drag at the shoulder of the primary and secondary bevels. It basically combines the strengths of the other grind types, with ease of touching up the edge (for the majority of folks who sharpen their own knives) when it's required.
The larger choppers also have CPK's S-grind, which through lots of testing (especially with the Bladesports choppers, where seconds and fractions of seconds, count), help pop the chips when chopping wood, and experience less binding when chopping deep.
If you've ever chopped a lot of wood with different axes, machetes and large knives, you'll have noticed that some of them bind in the wood a LOT more than others. Some of them need to be pried/worked out of the cut on every deep chop (obviously, the type of wood/material being chopped also plays a role in this). Nathan tested various types of grinds and his solution minimizes binding and aids in popping the wood chips free, well enough to have won numerous (and still counting
) competitions already.
If you want one heckuva large knife for chopping, I absolutely wholeheartedly recommend the Behemother. It has the grinds and design features Nate uses in the competition choppers, and more mass and length. It's one heckuva chopper!
