I think opinions also vary on that one, and effectiveness of anti-ship missiles vs carriers has obviously not been combat tested -- a carrier group has a lot of means to defend against cruise missile attacks though, the aircraft themselves being a pretty major one. There have been developments on both sides of that equation, but I doubt anyone who actually knows much about the current state of affairs is going to tell us :)

One problem with the missile strategy (which is the one Soviets tried) is that even if you might be able to cost-effectively attack a carrier group with missile cruisers, they are pretty much useless for anything else.