The USN and PLAN face dramatically different geographic circumstances and restrictions. The PLAN's potential theaters of conflicts will be near Chinese shores, the defense of which will be carried out by land-based J-20s. The carriers are designed to protect Chinese shipping lanes, especially portions that traverse the Middle East / IOR and Africa; for these potential opponents, range and individual bomb load matters far less than versatility and tactical flexibility.
On the contrary I would argue that range/endurance and armament load are very important for Chinese carriers operating in the IOR. In that region, China will face regional navies armed with impressive 4+ generation and even some 5th generation fighters of their own that will be operating from home air bases. In that region China will face a similar dilemma to what USN carriers operating in the western pacific face -- i.e.: which is the need for long range, persistent combat air patrol.
We've of course been over the small number+longer range vs big number+shorter range balancing issue for carrier air wings.
For a carrier J-20 vs FC-31 derivative match up, it all depends on how the numbers carried vs range balance lies.
For example, on a given carrier, if a J-20 has a 50% greater range than FC-31 but said carrier can only carry 80% the number of FC-31s, then one could make an argument for J-20 over FC-31.
But if the J-20 has only 20% greater range than FC-31 and can only carry 70% the number of FC-31s, then it might tilt more towards FC-31.
Aircraft are tailored to their vessels, rarely vice versa.
Yes and no, it depends on what stage of development a carrier is at and what stage of development an aircraft is at. E.g. at this stage, if the Navy is still unsure of whether they want a J-20 or FC-31 derivative, I expect they will have specced 00X's elevator and overall flight deck in such a way which can accommodate the likely dimensions of both a J-20 derivative and an FC-31 derivative.
Just how long would it take for the J-20 to reach that level of economy of scale? If you are premising that the naval order for the FC-31 won't be significant, just how big would a naval J-20 order be (hint: less since each ship would carry fewer J-20 vs FC-31s)? Have we accounted for the fact that the J-20 will be bigger in most aspects (larger radar/weapons/engines/etc.) which will significantly drive up the price?
Land based J-20 orders + carrier based J-20 derivative orders would likely lower production costs overall in common components, versus an order of only carrier based FC-31 derivatives, even when factoring a plausible multiplier for the fact that a smaller number of carrier based J-20s will be bought than if the navy chooses a carrier based FC-31.
The problem with a carrier based FC-31 is that it the Air Force is not interested. If the Air Force is intending to buy an FC-31 derivative as well then that would change everything. But the Air Force isn't and looks less likely to by the year, so if the Navy chooses an FC-31 derivative for its carriers, then the Navy alone are basically going to own the entire unique type of aircraft.
The FC-31 is lacking subsystems, which could be installed with relative ease, but it seems to me that its design is near finalization, judging by its closeness to the scale models. Additionally, SAC is still putting out the claim that it can get a production FC-31 to fly by 2019. In fact, given that the FC-31 has dual front wheels and that SAC has far more experience in the R&D of carrier-based jets than CAC, the FC-31 will have a much smoother transition to a navalized model than the J-20.
I think there is a compelling argument for why the PLAN may seriously consider both a J-20 derivative and an FC-31 derivative for its carrier based fighter, but I find the idea that the FC-31 will somehow have a "much smoother transition" to becoming a developed navalized fighter, to be rather hard to believe.
As far as we know, neither of the two flying FC-31 airframes are flying with any form of subsystems integrated into their airframe.
J-20 otoh by this point should been flying, testing and operating with early production level avionics and weapons systems and datalinks for years now, across at least 8 prototypes and anywhere up to a dozen or more serial aircraft by now.
Any carrier based derivative of J-20 will be able to leverage from the subsystems of the land based J-20 that will be much more mature than the nonexistent subsystems for FC-31 by the time the Navy gives the go ahead for one of the two options to be chosen.
Both J-20 and FC-31 would have to undergo substantial airframe modifications to accommodate carrier operations.
FC-31 does indeed have "twin nose gear" -- but that is like talking about the icing rather than the cake when we think about the rest of the modifications that the overall airframe that both aircraft will have to go through... folding wings, strengthened nose and rear landing gear, catapult nose gear, anterior and posterior strengthening of the airframe, developing more corrosion resistant skin, and of course integration of a talk hook.
I would say the only slightly compelling premise for the idea that FC-31 might have one area of advantage in development is that SAC has already developed J-15 so it has more experience than CAC in developing carrier aircraft, however considering the overall competency that CAC has demonstrated over the last decade I would be surprised if CAC is unable to compete in this area.