A couple references I looked at claim that cyanide case hardening produces a higher surface hardness than charcoal pack hardening because the cyanide process nitrides the surface as well as carburizes it. I don't know if this is true or not, and one source said that it was tough to prove by Brinell hardness testing because the hardened skin was so thin that it would deflect under the point of the Brinell tester due to the softer material underneath. There is also a lot of conflicting and very obviously incorrect information on the cyanide process, but what KY Jon posted seems accurate and explains why it was less costly than bone pack coloring. I'd like to confirm the part about nitriding of the surface but it can be seen that nitrogen is certainly available.
Apparently, both time of exposure of the red hot steel to a carbon source and pressure affect the depth of carbon penetration. It is claimed that there will be a slight pressurization with a tightly packed crucible with a very small vent hole which will cause deeper carbon migration, as will heating in a pressurized carbon rich atmosphere such as a carburizing flame or a furnace rich in carbon monoxide. That made me wonder if that has as much affect upon the resulting colors as the composition of the charcoal pack, i.e. bone charcoal, willow charcoal, charred leather, charred fruit pits, etc.? I'm interested in what might have been different in producing the deep predominantly blue colors seen on original Lefevers with lots of remaining case.