There is much confusion with the term CCC or CC. Any hospital can call themselves a Comprehensive Cancer Center or Cancer Center for that matter, and there is no trade name for such. There are organizations such as NCCN, National Comprehensive Cancer Network and NCI, National Cancer Institute, that have their own approved listing, as well as U.S. News Report's Best Hospital listings in Cancer, ENT.
The two you mention, NYU and Mt. Sinai are both top cancer hospitals, especially in ENT, and are on the above lists, and I go to both, in addition too, Beth Israel, which is part of Mt. Sinai now.
http://www.nccn.org/members/network.aspxhttp://www.cancer.gov/research/nci-role/cancer-centers/findhttp://health.usnews.com/best-hospitals/rankings