The force to trip is calculated into the breaker design. An overload condition on either leg will trip both sides of a double pole breaker.I would not use a double pole for two seperate circuits. One reason is the mechanical force to keep the breaker closed is double that of a single breaker (harder to trip, i'd assume?). I just don't see the reason to even bother doing it that way?
I run multiwire circuits all the time, where both legs of a split phase panel are fed on a 4 wire feeder with a shared neutral. It is required to tie BOTH hot phases to a double pole common trip breaker on these circuits, so if one is off, BOTH are off.