There are safeguards to protect against what you're describing - hijacking of another webmaster's website. Just remember that, when you change domains (and every subdomain is a separate domain), browsers WILL display the new domain to protect the copyright of the displayed domain. Frames can be made to work as well as AJAXing content which is pulled from subdomain but that's not the wise way to go.
IMHO, the best solution for you would be to PARK newdomain on the directory of the sub.domain.com - assuming that you own/control/host both domains.
Yes, ServerAlias may work but ONLY if you have control over the server and/or virtual host file (which most webmasters will never have ... until you get to dedi and, maybe, VPS).