Truth vs hype
Yes, IN has operated carriers for decades and is therefor „generally“ more experienced, but the STOBAR layout of Viki or IAC1 is a new one, which needs to be trained first as well and PLAN is already doing this, from the carrier itself! They also train with foreign navies (Brazilian navy) to gain more experience wrt carrier operations. When we look at it rationally, IN and PLAN will start at the same level when it comes to STOBAR carriers, AEW helicopters, IFR via buddy refuelling...,
Yes, J15 can't take off with full payload, but neither can the Su33, Mig 29K, N-LCA or the planned Sea Gripen:
...According to Peter Nilsson, Gripen’s Vice President of Operational Capabilities, the Sea Gripen is intended for both CATOBAR (Catapult Assisted Take Off But Arrested Recovery) as well as STOBAR (Short Take Off But Arrested Recovery) operations. “There will obviously be differences in the MTOW (Maximum Take-Off Weight). In a CATOBAR concept, the Sea Gripen will have a MTOW of 16,500 kilograms and a maximum landing weight of 11,500 kilograms. In a STOBAR concept it depends on the physics of the carrier. Roughly, the payload of fuel and weapons in STOBAR operations will be one-third less than the payload in CATOBAR operations. There will be no differences in ‘bring-back’ capability,” he says...
Saab offers naval Gripen to India | StratPost
That's the problem of taking off via ski-jump, that's why these fighters will carry more weapons or fuel tanks and less fuel at the take off and will be refuelled, in the air again.
Yes, the Liaoning is the better carrier and will have the better carrier fighters, but it's main aim will not be to project power to the Indian Ocean or to attack India, but to defend Chinese coast lines and areas of interest in the east, just like Viki and IAC 1 are not meant to project power towards China, but to defend Indias coast lines and areas of interest around India. Therefor, PLAN will have to compare it's capabilities compared to USNs carriers and their fighters, which still have clear numerical and technological advantages.
However, one has to understand that the main aim of both navies and the both carrier (of IAC1 as well), is not power projection towards India or China, but mainly coastal defence and control of the areas of interest around the mainlands and islands!
Therefore Viki and IAC1 will be used to cover the Arabian Sea and the Bay of Bengal, while Liaoning is aimed on the Sea lanes at Chinas coast line (which then aim on more capable USN carriers btw).