ComangliaQuicksync is nice cause it's hardware encoded by the iGPU that you're not using at all and produces a slightly better video quality than the hardware encoded nvenc (assuming same video settings).
QuickSync is a dedicated encoder. It doesn't run on the iGPU itself, but rather a small core sitting next to the iGPU.
Quality depends on what generation of QuickSync you're running, Haswell or later tends to match NVENC. QuickSync in Sandy Bridge was garbage, and in Ivy it was decent.
ComangliaQuicksync is a Intel thing though and I'm not sure how supported AMD APUs are.
Just like NVENC, QuickSync is actually a dedicated hardware encoder. It requires the hardware to be on the CPU die itself. It obviously isn't on AMD CPUs. It's only on 2nd gen or later Intel Core CPUs with onboard GPUs.