Microsoft came up with DISM that solves this issue entirely... DISM doesn't care about partition size but, obviously, you must ensure the backed up data will fit onto the smaller disk - i.e. Don't knowingly try to put 500GB worth of C: onto a new 250GB disk.
DISM is available through the WAIK (Windows Automated Installation Kit) kit and you can create bootable media so you can begin using such tools as DISM and DISKPART.
DISM captures only the files/folders in use and doesn't have any knowledge of the partition structure used.
DISM creates a .wim file that is essentially a compressed file but it retains all the files. folders and attributes/permissions on the original install. As an aside: 7-Zip now has the ability to open .wim files so, in an emergency, you can easily extract files/folders from a different computer.
When using DISM to restore the image you must pre-create the partitions you require (using DISKPART to create (a basic example) the system reserved partition and then the main C: partition) and then you can put the WIM file into your new C:. It is then recommended you then use the BCDBoot tool to copy the Windows boot files to the boot partition (System Reserved) which will allow your Windows installation to boot.