I use Robocopy not so much for the speed of transfer, but I noticed using Explorer to do large transfers slows down my Windows Explorer.
Robocopy in addition to not using Explorer, has the ability to resume transfers, so if there is a problem or I need to pause or abort the copy. I can pick the transfer up without needing to recopy all the files.
Third party copy utilities say they use larger transfer buffers than Windows, however, I personally don't usually notice a difference. It really depends on the type of data (i.e. a lot of small files, vs a few big files) if the buffer sizes seem to help me.
In the end, I look for feature like (resume, logging, error handling...) rather than speed.
I assume Robocopy has low overhead because you can turn the updates to the command line off, and there is no GUI to eat up CPU time. Some say using the multi-threading switch helps, but if you only have one source disk and one destination disk, I'm not sure if that will help because the drive heads will be swapping between files. I believe one file at a time would work best for one set of heads.