It's the same thing. Moving heat out of the GPU chip faster results in it running at a lower temp.
At steady state, heat is transferred into the heatsink at the same rate the heatsink can dump it into the air. However, that steady-state rate is only fixed for a given GPU and air temperature.
The concept of "heat soak" is only something that applies during the warm-up transient. Before the heatsink reaches its steady state temperature, it can absorb heat more rapidly. Once it hits that steady state, the rate at which it can absorb heat from the GPU will level off somewhat, but it doesn't get "overwhelmed".
Even once a steady state has been reached, it doesn't mean the heatsink cannot absorb more heat, but it will only do so if the GPU gets hotter. If/when the GPU temperature increases, the rate of thermal transfer into the heatsink will still increase and the rate at which the heatsink dumps that heat into air also increases (i.e. because the heatsink will also get hotter). This follows from
Newton's Law of Cooling, which stipulates that the rate of heat transfer is proportional to the temperature difference.
Sure, a better heatsink could benefit more by reducing that bottleneck between the GPU and heatsink.