In order to destroy a carrier, enemy must be able to penetrate the carrier's own defence network of frigates destroyers subs & also the aircraft from the carrier. Its not that easy to fire a missile at a carrier and destroy it.
If a enemy carrier battle group is sighted and you don't have enough fire power then first thing you have to do is pick out your vallet an see your family photo thinking that it may be last time.
Next thing make a decission either to face the group or to flee from the group which is not that easy cause the aircraft are fast enough to out run a ship
In another scenario if two carrier groups come face to face each other then it will be a damn hell of a show. Obviously the one with more fire power wins. Also depends on picking up vulnerable targets first to create havock in enemy's mind.