The original cross is Cornish/Plymouth, but the 'Cornish Cross' chickens today are far developed beyond that original crossing. If you were to perform the cross yourself, you'd get a good meat bird that can free-range and develops to meat capacity within the first year of life. I'd highly recommend doing the original cross, as free-ranging improves meat taste drastically.
The genetics in modern 'Cornish Crosses' leads to a very unfortunate animal that reaches it's harvesting weight at 8 weeks or so, and often cannot survive much past that point, or breed on it's own. I personally can't stand even looking at them because I feel they're such a violation of good animal stewardship. Just my opinion and personal view of them though.