Copy SQL DB files/backups
I can recommend to use Robocopy, it has the support of multi threaded copy. And it won't take ages to calculate the packages before.

Your syntax would be as follows:

robocopy "C:\SOURCE\Folder\folder" "D:\folder\destination" /mir /MT:XX

I use the mir option, since it will copy everything, meaning doing a perfect mirror. So you don't have to worry if your copy job stucks for any reason. You can easily run the same command again and it will only copy the missing files.
Be careful if you have hidden files in your folder, for example if you have the files placed directly on your Drive root folder. Than you will have problems copying the recycler ;)

MT Parameter
The Command /MT will run your copies with multiple threads. You can choose a number between 1 and 128, default is 8.
Please read : msdn Robocopy

Also one advice is to copy from the machine with more CPU Power since a copy job will alwas run on the CPU where you are currently logged in. In most cases I copy from the destination server, since it is probably not in use so far.