The reason they chose Russian Navy chose Mig 29k because of the following reasons:-
Now in a war scenario, Mig 29K will prove more effective because navy will be using it in striking mission which is it's specialty. Su33 is not a attack fighter and failed even to impress Russia to use it in present day war scenario. It has older avionics and 8g(J 15 has 9g) maneuverability compared to 12g of Mig 29K.
Thrust to weight ratio:
j15 - 0.83(0.87 speculated with newer engine but have no confirmation)
Mig 29K - 0.97
Range
j15 have combat radius of 1000 km compared to 700 km of Mig 29K but in war fighters don't go more than 300km - 400km radius away from it's carrier. And again China will not use Su 33 to attack on Indian soil.
Payload
j15 can carry 9 ton payload as against 6 ton of newer Mig 29K for Indian navy. Odds in favour of j15 in this case.
RCS
j15 has a very large RCS of more than 5m2 as against 1m2 of Mig 29K which Indian Navy is currently using(Note:- RCS of Mig 29 used by IAF is 2.5m2 not to be confused.) Thus, any IN ships can detect j15 from distance above 200km away as opposed of Mig 29K which can only be detected when it is 50km-70km away. But BVR missiles can target a ship from more than at least 110 km away.
(Note: 290 km range Brahmos cann't be fitted with Mig 29K,thus cann't be considered.)
J15 is a heavy class fighter,
thats the reason it cant be turned around immediately and sent back in battle
as it needs heavy maintenance as compared to the lighter MiG-29k
this was figured out by US navy first, hence they opted for a lighter fighter
replacing the F-14 with F-18
2nd was the IN with more than 4 decades of experience of operating CSF
IN choose to go for MiG-29k, China on the other hand is a new comer
and is certainly not aware of this fact in practical terms.
Russia too realized the same in discussions with IN and choose to go for a lighter MiG-29k
in comparison to Su-33 as a result Su-33 assembly line was shut down and dismantled.
<j15 is copied from a Ukranian prototype going by jf17, j11 and j16(su30mkk copy ... unbelievable isnt it?
) I expect avionics to be 70% of what mig29k is. As for AESA these frauds are using a planar radar calling it AESA.