QuickSync is a hardware encoder which means it is limited in its capabilities. If they are not available on the chip, they cannot be added later. Only driver tweaks are possible. X264 on the other hand runs on the normal CPU and can be programmed with new functions to improve quality etc.
So the first thing you have to know is that QuickSync quality depends on the generation of QuickSync you have. With one of the latest Haswell chips the quality has become quite good and is nearing X264.
The main benefit of a hardware encoder like QuickSync is the offloading of cpu usage to the hardware chip to do the video encoding. So if you are limited or have a very CPU intensive game/program running, it can be very useful. Also to make local recordings without really noticing any load.
Now I already answered your question about headless on the other thread, but yea, you need to have a monitor or fake monitor connected to the iGPU in older versions of QuickSync.
To show you a quality example (this was done with the latest haswell generation) see this post:
https://obsproject.com/forum/threads/how-to-use-quicksync.16664/#post-96945
