the Chinese have a series of big long range anti ship missiles - their obvious use is to keep the USN at arms length and, if possible, deny the Taiwan Strait to any carrier battle groups
relatively recently they have been developing a ballistic missile (rather than a cruise/Exocet type missile) to do the job - this could push the USN well out east of Taiwan
the Varyag has been sitting in China for years - the real problem they have however is that they cobble together systems from all over the place - some are developed locally, some bought in from the russians, french & brits, and some are "reverse enginneered" or just straight stolen
Given the problems that the Brits, Russians and the yanks have in making their own kit work (Nimrod AEW anyone??) together you have to have some real doubts as to combat effectiveness of the Chinese ships
In fact her latest destroyers appear to be a step back from the last lot in terms of weapons/systems fit and some people think they got too ambitious
you can buy a lot of missiles for the cost of one carrier