I'm no military expert by a long shot, but aren't aircraft carriers these days pretty much the equilvalent of battleships in WWII? Too expensive, too vulnerable and designed to fight the last war. A main function of aircraft carriers these days is to "show the flag" which could just as easily be accomplished with a training carrier.
If your objective is to project power from the sea and conduct expeditionary warfare then aircraft carriers are most certainly not obsolete. The Falklands War is a perfect example of a relatively modern conflict that could not have been won without carrier based air power.
OTOH if your only objective is to deny a certain area of the sea to others then other weapons like subs, mines & relatively cheap missile platforms are probably a much more economical way of doing that. If China simply wants to keep the US Navy away from say, Taiwain then yeah, carriers probably aren't the way to go. If they want to go out and have the ability to seize islands in the South China Sea then they'll want carrier based airpower.