This is much different than with piston engines, which also have propellers, but are much different mechanically. Turbine engines are safer and more reliable than piston engines, which are typically found in smaller aircraft.
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Turboprop vs Jet SafetyBoth turboprops and jets are powered by turbine engines, so they are essentially the same thing and thus, are considered to be equally as safe.
Planes with turboprop engines are typically limited to a lower cruising altitude than jet engines, capping at around 25,000-30,000 feet. Because of this, turboprops are also more susceptible to turbulence, noise, and inclement weather.
Turboprops simply cost more: to buy, to own, to fly. They offer better performance, reliability, and lighter engine weight. They also scale up well. After the initial premium for switching to turbines, cost per seat starts to go down.