Edge retention has several components:
Wear resistance: the ability to retain a sharp apex when cutting abrasive materials. Generally, high-carbide powder steels will greatly increase wear resistance. Check out Anderson's thread to get actual numbers.
Resistance to rolling: Cutting hard materials can roll an edge. Generally, resistance to rolling and deformation is a function of strength, which itself is a function of hardness. Most high-hardness steels in the low to mid 60s Rc will resist edge rolling far better than soft steels in the 50s Rc.
Resistance to chipping, cracking and breaking, known as toughness. Lots of factors affect toughness, but usually softer steels and steels with lower carbide loads are tougher.
Geometry: Thinner geometry is often a huge asset in how long an edge will last, but a lot depends on what you are cutting. Anderson's thread has good information on this, too, with actual numbers. Thinner geometry is also easier to sharpen. The results you see in Anderson's epic thread are based on rope cutting. Those results will be different, sometimes a lot different, if you're cutting different kinds of material.
Edge stability is a combination of toughness and strength, but toughness and strength are usually at odds with each other -- increase one and reduce the other. There are steels processing techniques that can increase both, but the toughness steels are not likely to be the strongest steels. Edge stability requires a balance of toughness and strength that is the best balance for the material you are cutting.