Like others have said there are many different considerations, usually you would brief your approach, weather, terrain, notams and threats with your other pilot.
for example, when I’m flying into Aspen my main consideration is the weather and terrain. So if I loose one prior to LIFT I’m diverting, between LIFT and CEYAG I’m executing a missed approach. But after CEYAG I’ll probably land that bird one way or the other. Cause there is no way in hell I’d want to do the single engine balked procedure.