The point I was making is that Rockwell hardness, which does in fact measure the force needed to deform steel using a penetrator, does not accurately predict plastic deformation as it might be experienced by a knife edge. In the case you cite, I would expect CPM-3V to experience plastic deformation and 440C to experience brittle failure when they are both pushed to their limits. The "limit" for CPM-3V will be higher than that for 440C, however.
Hardness is not strength. And that's where the simple solution of finding a steel that can get hard but do so without a lot of carbon falls apart. That's why people competing in the Professional Cutting Competitions are not using low alloy steels.
There are lots of different things that are commonly called strength, and we need to clarify what we mean, or we end up talking around in circles.
Two of the strengths are materials properties. The first is yield strength, which is the amount of stress required to create 0.2% (or 2 parts per 1000) permanent deformation in the metal. Yield strength is related to load required to bend a knife or roll an edge. Rockwell, Knoop, Brinell, and Vickers hardness values have been successfully correlated with yield strength; therefore hardness can be used to assess yield strength.
The second strength that is a material property is ultimate tensile strength, or UTS. UTS is the amount of stress required to cause the metal to break (generally "engineering stress", not "true stress", but that's another story). Hardness tests cannot be used to measure ultimate tensile strength.
One of the challenges related to knives and strength is that we sometimes don't distinguish between yield and ultimate strengths. For soft steel (steel that is far from its maximum possible hardness), there is a big difference between the yield strength and the ultimate strength. For hard steels (steels that are close to their maximum possible hardness), there is almost no difference between the yield strength and the ultimate strength. Thus, a soft steel will permanently bend substantially before it breaks, and a hard steel will have almost no permanent deformation before it breaks.
Note that the comment above refers not to absolute hardness, i.e. a RC value, but relative hardness (the actual hardness compared to the maximum possible hardness). And it's a bit of a generalization. But it helps to understand some of what is going on in knife edge performance. If one steel (probably 440C in your example) is closer to its maximum possible hardness than the other (probably CPM-3V in your example) at equivalent hardness values, it's more likely to chip while the other is more likely to deform. That's because the yield stress is almost the same as the ultimate stress, and when it gets to the bending point, it breaks.
Another meaning for strength is "edge strength", which isn't a material property at all, but a combination of the yield and ultimate strengths of the material and the geometry of the edge. The edge strength is generally not well defined, but generally refers to the ability of the edge to avoid damage in response to some kind of usage.
A final strength that is sort of a material property is fracture toughness. Toughness represents the ability to withstand fast fracture. Fracture can occur at gross loads below the yield and ultimate strengths of a material, due to the presence of flaws. For example, in the "famous" YouTube video of the salesman whacking a "katana" sword against the table, only to have the blade snap and the broken piece bounce back and hit him, the blade was not stressed beyond its yield point, and most likely not beyond its ultimate strength. Rather, the impact caused a high load in the area where a flaw existed, which caused the blade to break.
The reason I say that toughness is "sort of a material property" is that the most commonly used measure of toughness, Charpy Impact Energy, doesn't directly measure toughness. The best test for directly measuring toughness, using a pre-cracked compact tensile specimen, only works in thick steels. So you couldn't measure the toughness of a knife blade; you could only measure the toughness of the steel the knife blade was made from, but in a different geometry. Because of this, toughness is extremely difficult to quantify and use in a knife.
Bottom line: Hardness measures yield strength. Fracture tendency is related to the difference between yield strength and ultimate strength. Toughness is difficult to measure, but if it's too low, blades will break under impact loading. Both blade and edge strengths are combinations of material properties and geometry.
If we want to avoid confusion, we probably ought to be careful about which type of strength we reference when we say "strength".
Carl