I moved one subdomain to another server with scp and some new A records.
I copied the site in two operations which gave me a chance to look at what I was moving with my laptop file browser.
I checked that the site looked ok as a subdomain of the new site. Then moved it to its original domain name on the new server.
It took some effort to get chrome to let go of the old address even when dns had propagated to my laptop. I'd heard it would often resolve its own way. Firefox and Safari caught on to the change much faster.