Trish,
I'm sure that the ability to cope with emergency situations increases with training levels and experience.
Professional pilots deal with an emergency from a checklist and rationalise it. If we panic, we die. A prime example of dealing with a major emergency by not 'panicking', and particularly one not in a checklist, would be the Sioux City crash where many lives were saved.
We do not sit on the flight deck and lose our heads completely. In a commercial ( ie: pax carrying flight there are two crew anyway. One person alone may be more incined to lose control)
In the two incidents I have been involved with in 10 years of flying, no-one 'panicked'. We used our training to resolve safely two potentially dangerous situations. A bit like Pavlov's dogs perhaps.