You'd expect those two fighters to be sort of on par to be honest. Until you consider any requirement for range or payload. Or if you have a limit on cost. J-10C probably wins out on cost, serviceability, maintenance. J-16 wins out on range and payload. Some missions require range, some require carrying heavy ordinance. Some situations require lower cost and high serviceability.
J-10C has much lower RCS (even with efforts to apply RAM to J-16) you can cut 15m^2 to 5m^2 but it's still not comparable to 0.5m^2 for example.
J-16 has much better payload and available energy. BVR sort of evens out a bit.
WVR probably goes to the J-10. While the flanker is remarkable, the twin seater is less of a performer and the uncropped delta canard is an agile thing with a smaller visual signature.
This is not very surprising and in this day and age I don't know how any informed PLA or military watcher can be a certain company's "fanboy" when comparing aircraft of the same generation with access to the same avionics and weapons suite.
Sensors, fusion, networking, situational awareness, weapons, ECM are the most impactful determinants of overall net capability/competitiveness for any two modern fighter aircraft of the same generation.
J-16 and J-10C most certainly are in the same generation with access to the same scope of subsystems that the Chinese aerospace industry can offer, and uses many of the same key weapons systems.
So it's entirely reasonable that J-16s and J-10Cs and are evenly matched in many domains, assuming any DACT they do is on "equal" rules of engagement.
From there the only differences are physical and monetary; range, payload, number of crew onboard and cost of procurement and maintenance -- but in small scale (1v1, 2v2 or even 4v4) DACT, those factors would be far less important anyhow.