As far as their relationships with John Wick go, Winston definitely cares more of John’s well being than The Bowery King.
So while Winston will hopefully still be supportive of John in John Wick 3: Parabellum, there’s no guarantee The Bowery King will follow suit.
The Bowery King, on the other hand, only helped John in Chapter 2 because if Santino gained more power, his operation would eventually be kaput.
Granted, Winston was forced to tell John at the end of John Wick: Chapter 2 that he’d been declared excommunicado by the High Table for killing Santino D’Antonio on Continental grounds, as well as call in that the bounty on John’s head had been doubled and offered globally.