Note that I said "You can get a shaving edge with almost any angle.", not a razor edge.
Sharpness and cutting ability are two completely different things...

Examples:
Note...For all of these, I am assuming,
1. A complete penetration cut(where the blade is completely covered by the material being cut).
2. A push cut being done, as slicing is a COMPLEATLY different subject.

Cutting cheese:
Wire cheese cutter...
Cutting ability A
Sharpness F
Hair popping sharp 3/8" thick survival/combat knife...
Cutting ability F
Sharpness A-
Straight razor...
Cutting ability B-
Sharpness A+
Mora Knife with true single bevel edge...
Cutting ability B-
Sharpness A
Medium thick Convex edge...
Cutting Ability B
Sharpness A-


Cutting wood:
Wire cheese cutter...
Cutting ability F
Sharpness F
Hair popping sharp 3/8" thick survival/combat knife...
Cutting ability D
Sharpness A-
Straight razor...
Cutting ability C
Sharpness A+
Mora Knife with true single bevel edge...
Cutting ability A-
Sharpness A
Medium thick Convex edge...
Cutting Ability A-
Sharpness A-

Notice how the sharpness does not change with the material being cut.
The cutting ability changes dramatically though.
Now those were just averages...
The harder the cheese, the less well the wire cutter will work.
Cutting ability(once the SURFACE is broken by SHARPNESS), is almost completely determined by two things(or three, depending on how you count one of them)...
1. The smoothness of the area of the knife in contact with the material being cut(mostly the sides of the edge).
2. The Geometry of the blade, including the thickness and height of the blade.
If you include smoothness in with Geometry(as it is just the micro-geometry of the metal after all), you could say that it is almost ALL, the Geometry of the blade, that determines the cutting ability of a knife.
Every transition of a flat surface to another flat surface is like a wedge stopping the blade from penetrating.

The wire cheese cutter has almost no surface area, and, because the cheese requires almost no sharpness to penetrate the surface, it can cut VERY easily in the cheese, but cannot cut anything harder very well at all.

The hair popping sharp 3/8" thick survival/combat knife can penetrate the surface very well, but QUICKLY succumbs to the friction from the cheese, and from the wedging effect of trying to split, rather than cut that is prevalent in this cutting, because of the thickness of the blade. The later effect is what causes it to perform badly against the wood also.

The straight razor will go about half way into the cheese and then rapidly bog down, as it shares the problem that all concave ground blades do, of not working at all well in materials that are thick at all, because of the way the blade quickly gets thicker. It is only saved by the fact that it is SO thin, and it's height is so small that it produces very little wedging force, and what little it does produce will tend to make the material stay away from the surface of the blade, further reducing friction. In wood, the result is close to the same.

The Mora knife with true single bevel edge will tend to wedge and bind a bit in the cheese, but is thin and low enough in height to still go through reasonably well. In wood it will tend to have the same advantages and disadvantages. Though not the easiest to push through wood, this shape has special properties for woodworking tasks that make it one of the best for bushcraft

The medium thick Convex edge, will, because is is designed to have smooth contact along it's entire surface, tend to have the most friction of all, but will not bind as much. The sticker the substance cut the worse it will perform, but in most substances, it will bind the least, making it one of the best general purpose profiles there is. There can be wide variations in the performance do to small changes in the geometry of a convex edge that can make it much more suitable to cutting tasks. For example, a Fällkniven F1 performs very differently than a Bark River Highland Special, which is a very similar knife, and which both have convex edges.