Why would you pay an extra $50 for a cooler rather than use the stock one that Intel gives you for free? Well the answer is pretty simply put by Tom's Hardware. The short answer is if you are not overclocking, then the Intel fan makes lots of sense
Great cooling for overclocking
It might not matter for some people, but for at low RPMs the Noctua is more efficient. It will cool to 26C at 1000 RPM while the Intel cooler is 50C.
If you are doing maximum overclocking, then at Max RPM. It will be noisy but will be efficient.
- Noctua NH-L12 heating +26C for 43.1dB of noise
- Intel cooler +35.8C (so right at thermal limits) for a little less noise of 40dB
At low noise, you can overclock
It's interesting to see that the heating at 1000 rpm which is much quieter basically has the same level of cooling:
- Noctua NH-L12 heating 26.7C at 1000 rpm (so slowing to 1000 rpm only is a 0.7 difference) but is much quieter at 36.8dB
- Intel cooler is basically not super practical at 1000 rpm generating >50C heating at 36.9dB
So the net is that the Intel cooler is louder at low RPMs and is less efficient (35.8C at maximum RPM), so the Noctua is way better and you'd want to run it at 1000 rpm and get be 10C more efficient on cooling. That won't matter too much unless you care about noise or overclocking.