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A Gulfstream V has a service ceiling at 51,000 ft so you'll be way above commercial traffic and most of the bad weather. The only thing you have to worry about is takeoff and the ascent if your departing city is nasty also and going down into the bad weather for the landing. King Airs I think have a service ceiling of 31,000 ft, so you're farther down the ladder.
In real bad weather I'd feel safer going commercial. 21% of fatal aviation accidents that are non-commercial flights are due to bad weather, so that's about 1 out 5 chances.
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