Re: David Krall response. The OP asked about paid pilots verses un paid, not 121 verses 91.
I suspect part 91 corporate flying may be more demanding than 121 for a major carrier. I do not know this and have no experience in any 121 flying. However, if you are hinting that private pilots flying for their own use has a more demnanding job than the corporate pilot then I must call BS on that.
I see threads on here a lot concerning whether a trip should or could be made. If you do not want to go then just don't go. Nobody else matters. I would think the pressure would be quite low. Of course many accidents for this group comes from poor decision making.
In the corporate world this is a little different. In the large departments with turbojets most are two pilot operations with a lot of support and aircraft that can get over a lot of weather. In the smaller departments as in turbo props it is normally a one pilot operation. You handle dispatch, ground transportation, maintenence, catering, fueling, weight and balance and the list goes on. In addition the pilot is very aware that the owner has spent $millions on the aircraft, perhaps another $30K per year on fixed costs, including the expense of sending at least one pilot to 3 days of sim school each year and another $1K per hour in DOC.
What this means is the owner wants to go when he wants to go. You get a call today that his wife and kids want to leave Friday afternoon to XYZ and return Sunday afternoon, you know you are going. You know she will be late, putting you into a strange airport at night, IFR and the FBO will be closed. No use even looking at the weather untill Friday morning because you are going. On top of that the turbo prop pilot gets to fly at the worst altitudes 180-280. You may be dealing with ice and/or convection, many times both at any time of the year. I see people talking about doing practice approaches, heck once I get to the approach I can relax, unless there is a thunderstorm over the airport of course
. None of the above matters, you are going and you are going to land at XYZ. If you want to feel some pressure get a corporate gig flying a turbo prop.
So, back to the OP's question: Why is this safer (or is it?) than private pilots in small planes. As I and others have said, equipment does play a part. Look at the insurance requirements for the rest of the answer. There is a reason they require a MINIMUM of 3 days a year in a simulator, require at least a couple thousand hours of flight experience and a few hundred in make and model. Also frequency of flying can be a factor. I recently retired from a great part time job because we were not flying enough for me to stay proficient. We were down to less than 100 hours per year. I suspect most fly 100-200 per year and this of course helps.
So to the OP I think in general (they are exceptions like some small piston 135 ops) the professional pilots will have a better safety record for a variety of reason that have been well stated in this thread by others.