The most important reason why men and women react differently to stress are the hormones. cortisol, epinephrine, and oxytocin. It used to be thought that the amount of Cortisol and/or epinephrine secreted by different sexes is different, i.e women secreted more cortisol. That has been proven untrue. The real difference is in the amount of oxytocin secreted. There is more oxytocin secreted in women than in men. Since oxytocin counters the production of cortisol and epinephrine, women and men tend to react differently and men tend to get more stressed than women.
In women, when cortisol and epinephrine rush through the bloodstream in a stressful situation, oxytocin comes into play. It is released from the brain, countering the production of cortisol and epinephrine, and promoting nurturing and relaxing emotions.
While men also secrete the hormone oxytocin when they're stressed, it's in much smaller amounts, leaving them on the short end of the stick when it comes to stress and hormones. Women will often react in a more rational manner by even befriending instead of fighting in a stressful situation because of this hormonal difference.