If the J-11BG has indeed received comprehensive avionics upgrades (essentially a J-16-lite, for the lack of a better term, or maybe the canceled J-11D without changes to the airframe), what utility does it really have? In a peer-to-peer conflict, say against the US Air Force, China already has more than enough 5th gens and 4.5 gens with J-20/J-35/J-16s to sling long range AAMs. The only utility I see is perhaps against lower threat adversaries (India, for instance, doesn't need to be countered with J-20s. J-11BGs and J-10Cs should be more than enough to neutralize the IAF), or some small conflict in SE Asia, or maybe just homeland security/defense (does China not have a "National Guard" of its own yet? Why not?). There aren't a whole lot of areas where a J-11BG would be used honestly.