An earlier post by OP (Weibo) claimed that the PLANAF requires a "medium-sized heavyweight" fighter, which OP defines as something comparable to the F-35 (i.e. 30+ tons MTOW while sporting similar dimensions). This means that the FC-31 design would have to be upscaled while the J-20 would have to be downscaled. Downscaling the J-20 could very well negate the range & payload advantage it had over the FC-31, as well as force it to adopt twin medium-thrust (or 1 x large thrust) engines.
Considering that SAC has far more extensive experience developing naval aircraft and the associated hardware, such as landing gears and catapult-compliant equipment, a competition between an enlarged FC-31 and miniaturized J-20 would almost certainly tip to SAC's favor. Other things being equal, of course, such as the production capacity of the two companies and the price.