To use rsync its very similar (could be the exact same) as scp but with rsync you can also copy permissions which may or may not be nice. To do that use the -a flag (it's for archive mode, which creates an exact duplicate...permissions and all).
The useage would be:
siteA = non-DH site
siteB = DH
Login to siteA via SSH and go to the root of your website(public-HTML). From there:
rsync -avr ./ siteBuser@www.yourDHdomain.com:/home/siteBuser/domain_directory/
the -a flag is for archive mode, the -v flag is for verbose mode (so you can see what it's transfering), and the -r flag is the recusive mode so it will transend into all the different directories.
The "./" is copying everything from that directory down the chain.