Slow image restore from one partition to another on the same drive.

Three cases here:

Case 1:
Samsung entry level AMD laptop bought in 2011. Image backup of partition C (30GB) to partition D on the same physical drive is quick, takes 10 min. Restore is quick too, takes about 25 min.

Case 2:
Asus mid-range i3 laptop bought in 2012. Image backup of C (30GB) to D on the same physical drive is quick. However, restore takes 3 hours!
My solution is to copy the image folder to an external HDD and restore partition C from that external HDD instead (with USB3.0 drivers loaded during restoring). it takes 8 min to complete restore.

Case 3:
Fujitse mid-range i3 latpop bought last month. It's the same case as Case 2.

My question: Do I need to load special drivers for restoring image from one partition to another on the same physical HDD?

Probably a controller difference between the different PC's. You found a solution - use a different drive.
It's not a good idea to keep the image on the same physical drive anyway.
Never heard of using different HD drivers.