Actually whats' most important is the application of the thermal compound to get it's full thermal conduction!
Both of what you list have their plus and minus, AS5 needs a long time to cure to it's best thermal conduction state, which means it actually needs a thermal layer for micronized particles to fully do what it is advertised and claimed to do.
IC Diamond needs a 50psi clamping pressure to perform optimally, (check their website for details), also IC Diamond has had many claims against them for heat spreader scratches from those moving the heat sink back and forth attempting to get better contact with lower pressure and scratching the CPU heat spreader, costing the CPU warranty. (Hello it's micronized diamond particles, and diamond is one of the hardest substances on the planet, of course it will scratch metal and cut glass as well!)
This is what you need to understand, the heat sink does the cooling, the thermal compound has no magical properties of cooling, all thermal compound is for, is to replace the microscopic pockets of air between the 2 metal mating surfaces, and that's all it is supposed to do.
No matter how shiny and smooth your heat sink base or CPU heat spreader appears to the eye, under a microscope in some situations it looks like the surface of the moon.
The finer the heat sink base is finished, the less thermal compound is actually needed to fill the air gaps.
So a thick layer of it is defeating the purpose of what it is supposed to be doing.
Too thick a layer of any thermal compound tends to insulate, instead of conduct the heat.
After all this time I am truly amazed at the abundance of ignorance that still abounds today regarding thermal compounds, with one claiming mine is better than yours when what is most important is the application of it, and the thermal footprint left behind.
I hope this helps you! Ryan