let's not forget the wings also people! wings need to fold or in the case of tomcats be in "overswept" position for hanger storage! F-15 is too darn wide for ideal carrier storage never mind the non-buffed up landing gears.
F-15 Wingspan: 42 ft 10 in (13.05 m)
F-18 wings folded - 8.38 m
F-14 Wingspan:64ft 1.5in 19.54m (unswept)
38ft 2.5in 11.65m (swept)
33ft 3.5in 10.15m (overswept)
Su-33 wingspan is 14.7m so...the F-15 has got nothing to cry about. The matter is the larger the aircraft is, the less you can carry, the smaller the aircraft is the more you can carry. But then looking at it the other way, the larger it is, the more range and payload it can deliver.
Er... yes. Of course an F-15 could do all that. But the problem is, the F-15 (navalise version) would be very large and an aircraft carrier might carry lesser of them. What we see is only the dimensions of the F-15, what about its weight when compared to the F-18? I would believe it would be much heavier too.
Plus, F-15 was from the start not designed for carrier operation, and to do that much modification to the aircraft would essentially mean designing for a new aircraft, not very cheap and cost effective to do it.
As for J-20, the arguement was the same as above... plus China's aircraft carriers are not as large as the US and seeing the first aircraft carrier that goes without catapult, I don't think aircraft fo J-20's size and weight might proof to be too useful (modified) on the deck.
Still don't think the J-20 will be serving on a carrier anytime soon. Ontop of that its a very large aircraft so the number of J-20 serving on the carrier will be small. Even the J-15 I think is too large for carrier operation.
The J-15 (if is even really called that) will be sufficient, currently the most advanced fighters serving on carriers are the F-18E/F, Rafale and F-35 (if it ever even gets into production). The J-15 with modernized avionics and weapons can hold it's ground. The Flanker heritage airframe is still very much potent in air combat.