Stobar carriers like Vikramaditya, Vikrant, 001,002 are just not where the game is at. They're very limited in scope of engagement.
1) No fixed wing Awac means extreme short sightedness( low helicopter range/speed, power of radar carried is also low) for very short period of time ( low helicopter endurance).
So how do you strike if you can't see the enemy more than 300 km from the CSG (200 km heli range + 100 km radar range)
2) Limited endurance/speed of carrier itself.(non nuclear)
3) Extremely reduced payload for aircraft ( although 80% of missions will be anti air, so not exactly the a limitation of the aircraft itself).
4) Small magazine capacity of the carrier.
(Nimitz carries more than 3000 tons of armament, Kuznetsov less than 500, also limited fuel for aircraft)
All in all, these stobars are just air cover for the ships that carry missiles ( cruisers, destroyers) and so perform a defensive role, while full strike carrier performs offensive role only and the attached destroyer squadrons are there for only defense.