It definitely varies based on who is writing it. Very, very little fiction subscribes to closed loop. Almost everything is open loop, with some branching thrown in for fun.

Oh and for grins, the stuff in the Arrowverse is a bizarre and inconsistent mishmash of the two, with artifacts of both whenever they think it's convenient. With the usual comic book logic behind it all. I swear, it's mostly there so they can feel free to rewrite anything they want with a wave of their hands. Though after awhile audiences get real tired of that.