Many times I've had to image/clone partitions of the machines across and SSH contection. Often there is not sufficient space to compress the whole image and transfer it over to the new machine and the desploy it inside that machine. This is very common with VPS providers.
Boot up both machines in single user mode or with a boot CD. I like using rescue CDs/OSs. Make sure all of the source partitions and destination partitions are unmounted or mounted read-only.