Both are made for very different roles; the BS is a trainer that can act as a regular fighter as well (and is way more capable as many much older types in service) and the J-16 is a striker.
Do you really believe J-16 is a striker? I don't think we have evidence to support such notion.
J-16s have been given to various units. Some of them past strike units but more of them being fighter units.
So I'd think J-16 is something like Su-30SM for the Russian Air force. That plane is spreading through RuAF like wildfire, often time replacing pure fighter machines. Including past MiG-29 units, some of which now use Su-30SM.
Similar thing could be said about Indian AF and Su-30MKI, which was received by a variety of units, many of them past fighter units.
So, just like those two examples, i think J-16 is also primarily a multirole plane. I'd expect its pilots to train for air superiority just as much as they train for strike missions.
Certainly, J-16 as a platform allows it. Alongside J-10B/C, it's finally the first true multirole plane Chinese have and actually use as a multirole plane. (Not sure how much Su-30MKK were used as multirole planes)