Anxiety-related gender differences are complicated. In general, for reasons that seem entirely unknown to researchers at this time, women appear to be twice as likely as men either to inherit and/or experience an anxiety disorder, wherever they are in the world and regardless of treatment status. One obvious difference is biology: female versus male hormones. Does the presence of estrogen somehow sensitize women to a heightened sense of panic, perhaps useful in an evolutionary way to protect the nest?
Cultural factors commonly appear as other sources of causation, looking at worldwide patterns in which it appears more socially acceptable for women and girls to experience fear as a symptom and to seek relief for it, while men and boys are more conditioned to avoid any display of this fear, or to counter it with reactive types of denial. Hence, men afraid of destruction may become hunters; men afraid to show pain may actively deny it when in the hospital.
Finally, it seems more likely that men may experience just as much anxiety as women but choose to deal with it in what they perceive to be more socially acceptable ways, such as substance abuse or violence.