I hate this argument. It's always the same. X beats Y, or Y beats X, or both beat each other. The reality is that such obvious extremities rarely exist. Also one can argue that the prevelance of multiple weapons and strategies to try and overcome the proven efficiency of an existing strategy merely prove that the existing strategy/equipment is a proven one.
People always seem to argue that a carrier can be destroyed because cheap aircraft/missiles, subs, land based weapons, satelites, long range ELINT aircraft and a surface group can be present to counter the carrier battle group.
Well lets get real here, a carrier battle group is expensive. But getting enough missiles, aircraft, submarines, land based weapons together to be able to overwhelm the escorts, the carrier, the CAP, the soft kill systems, the multiple hull redundancies (double hull is a common building practice on carriers) and everything else is NOT cheap.
Then finding the carrier is not easy. The commander of a CBG will not make it EASY. He will punnish every mistake you make while finding the Carrier battle group, and you will make mistakes. He will have other skilled captains to defence him. He has as much firepower as you do. It is concentrated in a very small area in a very large world.
GPS and Satelites may be able to locate a CBG at sea, but that depends on the location of the Satelite... which follows a very predictable flight path and can be shot down. It also depends on good weather, and numerous other physics based factors which as a physics graduate I can PROMISE you will serious mess up your operations.
Then you get together, you launch your attack. As you attack you WILL Be seen. You do not launch over 100 missiles and avoid detection. AMRAAM, Meteor, Sidewinder etc can all engage missiles. So the 40+ aircraft the Carrier has can be scrambled and engage you... after all to launch that many missiles without detection and without having already come across the CAP you will HAVE to be at long range. Even setting that aside an F35C can theoretically carry what... 12 AAM's. Say 4 ASRAAM and 8 Meteor. Even if you only have lets say 10 of your 40 F35's up in the air to engage in time thats still 120 missiles fired at the enemy missiles. Assuming a terrible 50% hit ratio, you knock down 60 straight away.
So 60 coming in towards your battle group. Your 2 T45's can engage up to 12 targets simultaneously but due to Aster having an ARH missile it can instead take time shared updates from the Sampson and rely on the ARH to engage more targets. Thats 96 missiles from both T45's. They are world beating missiles and come with a brutally effective sensor system. Lets say a very reasonable 75% efficiency for 69 more missiles killed.
Finally you enter local area defence. CAAM starts to open fire from the 2 T26 and the Carrier. Lets say a modest 24 CAAM on each ship. For 64 CAAM. And lets got for 50% hits due to closing speed of missiles, reaction time etcetc. Thats now another 32 missiles killed.
Finally the attack is multi vector to put the most stress on the battlegroup and because you want to ensure that if one attack group is found it doesn't mean your entire attack group is found. So 4 CIWS kills from the carrier, 2 from each of escorts for another 8 missiles killed so 12 from CIWS.
Finally the escorts will have moved to protect the CBG and deployed soft kill.
UMMMMMMm, You will need to fire over 200 missiles from multiple directions to even begin to start causing casualties to the CBG from maximum range. Thats assuming at most a 75% accuracy from the most modern sensors and SAMs available.
Assuming of course you find the carrier, engage at range with stand off missiles, the CAP doesn't find you, your satelite and GPS controlled missiles work...
Submarines are in my belief a FAR FAR greater threat to any carrier. Much harder to detect, it doesn't take as many torpedoes to sink or serious crippled a vessel. Torpedoes are more likely to hit areas like the engine room which means even if you don't finish the carrier you start bad fires, slow or stop it moving and numerous other bad things.
Carriers are not increasingly vulnerable. With concepts like UCAV and Stealthy fighters as well as stealthed warships CBG's are keeping up with the times. Networked sensor arrays and defence layers ensure that your likely to have to JAM the entire battlegroup to truly stop them from firing at you with a decent effectiveness. UCAV's are also very interesting X-47B can deliver 2 Tomahwak from a combat radius of 2000 nautical miles.... With the range of the Tomahawk added in they can easily strike with stealth and precision at long range high threat assets to the carrier. F35B's/Super Hornets carrier greater ordnance and are thus able to put up a very effective CAP in wartime. Not to mention SEAD and mass strikes to make it even more difficult to find the X-47B's.
Sorry, there is a lot of hype from both sides, there is a lot of real and historical proof of both sides. Which means they are both relevant and we will only find out which is more relevant in real life... which then also depends on the commander and so forth.
People always forget that more often than not, the most likely failure is in the human element of the strategy or equipment.