From an engineer's perspective, everything is defined in equation 1, 2 and 3 in this article: https://en.wikipedia.org/wiki/Heat_sink
So basically, in the case of a CPU, Q(dot) is the total dissipation rate, which is equal to the (thermal) power of your CPU. cp is the thermal capacity of air, which depends on various factors you have little control over (inlet temperature, humidity). m(dot) is the flow rate of your fan, which should be proportional (roughly) to its RPM and fan diameter. Rhs is the total thermal resistance of your setup, which is equal to (die to heat spreader resistance) + (thermal paste resistance) + (heatsink package resistance) .
So how does all this determine the heat dissipation performance? If you fix the air flow rate, CPU temperature (Ths) and air inlet Tair,in temperature, the only variables you can control to maximize the total dissipation rate are 1) lowering thermal resistance Rhs, which involves bigger heat pipe, better thermal conductive material, better thermal paste or deliding; or 2) increasing outlet temperature Tair,out. The later is achieved either through bigger fins, more fins, increasing total surface area of the fins, or optimizing airflow to maximize heat exchange.
As you might expect, all those optimizations have diminishing return, so the best heatsink will try to achieve all those optimizations simultaneously.
TL;DR: there's no single most important factor deciding the performance of a heatsink. There's no point using huge heatpipes on heatsink with insufficient fins area. Similarly, huge heat sink with insufficient heat pipes to carry the heat to the fins is also pointless (unless you want to intimidate spectators).