I use rsync. In the example below, example.com is the source remote server and howdy.com is the destination remote server. Run this command from your host machine:
ssh -o ForwardAgent=yes web@example.com "rsync -aze 'ssh -o StrictHostKeyChecking=no' --progress /srv/www/example.com/shared/uploads/ web@howdy.com:/srv/www/howdy.com/shared/uploads/"