All circuit breakers trip at their rated current. They pay attention to current, not voltage.
Circuit breakers have a voltage rating because the amount of current the breaker can safely interrupt is determined by the voltage. As you can imagine, a higher voltage creates a larger and longer arc which is more difficult to interrupt. In the worst-case the arc would not extinguish and the fault current would keep flowing even with the breaker open, at least until the contacts were completely burned away. Some larger breakers have a magnetic coil in series with the circuit that generates a magnetic field across the contact gap to help blow out the arc. Thus the higher the fault current, the larger the magnetic field.