accoring to wikipedia:
Anti-ship missile C802 weighs 715kg. its warhead weights 165kg. its attacking speed is 1.6M
DF21 weights 15tonne, speed is 10Mach. I failed find the record of warhead weight for DF-21D, which is reportedly to be "AC killer". the payload of old DF-21A is 600kg.
Being a ballistic missille, it's far more destructive and faster than any anti-ship missiles, and surely much more difficult to intercept. AC, though large in size, however is a smart target, for ballistic missile to handle indeed.
but of course, you are free to believe AEGIS can take all of them