Continuing with that line of thought, the cop who's had hundreds of adrenaline rushes is going to develop a higher baseline for what get's his adrenaline going. The citizen with a CCW may be a better shot, but how well does he manage the adrenaline? What is his experience making split second decisions under extreme stress? If you're planning on taking a shot in a crowd of people it's good to know what your limits are.
It's not always about who's a better shot. Being a good shot is important, I think we can all agree on that. But, just as important, is to know when to take that shot. Legally or otherwise.
People develop adrenaline baselines differently. That's really not the crux of the issue.
The average citizen (armed or not) is easy pickings for getting caught off-guard. They go about their day doing what they do and don't expect anything abnormal.
The police officer reporting in for duty is gearing up for his shift, and he/she knows that it can be anything but normal. That's where the education, training and experience comes into play.
Speaking for myself, I can't begin to count the number of adrenaline rushes I've had while working. But, I can and will say this. I never once took any for granted, or felt that they became run of the mill and affected me in some way as to make me less effective. Each and every one was a continuing learning experience.
I guess the point that I'm trying to make, is that it doesn't boil down to just one issue or ability. It's a multitude of training and life experiences that dictate how it all plays out.
You can be the best shot in the nation. But, if you freeze under pressure while someone is pointing a gun at you, it's all for naught. You could be a poor shot, but you don't freeze and you are able to fire back. At least you are able to engage the situation.