Maybe this will answer some of your questions. Back in the day (25 years ago) if you had a knife made from 440C you had a premium steel knife. Today it is just middle of the road steel compared to the "Super Steels" but still is a good performer for all around use. I think of the two steels you are wondering about 440C is better.
420 series contain several types with various carbon content between .15% and .40% this steel grade is widely used to make high end razor blades, surgical scalpels etc. It obtains about 57 HRC after suitable heat treatment. 420HC ( 420C ) is a higher carbon content 420 stainless. The HC stands for "high carbon" and it can be brought to a higher hardness than 420 and should not be mistaken for it. Buck Knives and Gerber Knives use 420HC extensively.[8] 420A ( 420J1 ) and 420B ( 420J2 ) are economical, highly corrosion resistant stainless steel grades. Knife manufacturers use this material in budget knives, also in diving knives due to its high resistance to corrosion.[8]
440 series has three types, 440A, 440B and 440C. 440A is a relatively a low cost, highly corrosion resistant stainless steel. In China, Ahonest ChangJiang Stainless steel developed 440A modified 7Cr17MoV, by adding more element vanadium.[31] 440B is almost identical to 440A, but has a higher carbon content range compared to 440A[31] 440C is considered a high-end stainless steel. It is very resistant to corrosion and is one of the most common stainless alloys used for knife making.[31] The once ubiquitous American Buck Model 110 Folding Hunter was made of 440C before 1981. 440C has highest carbon content in 440 group.[31] Böhler n695 is equivalent to 440C.
AUS-8 (8A) is comparable to 440B with a carbon content close to 0.75%.[8] AUS-8 is often used instead of 440C.[8] SOG knives uses AUS-8 extensively.
8CR13MoV & 8CR14MoV, actually these grades do not have very big difference. They are similar to AICHI AUS-8, an excellent value priced steel for its performance.