Actually, a turbo prop aircraft is powered by a jet engine which has propellers on it, while a biz jet engine doesn't. Let's compare the pros & cons of both aircraft types.
If you operate in rough or unprepared runways or air strips, the propeller driven turbo prop aircraft has the edge. Using a bizjet in this kind of enviroment may only invite FOD (Foreign Object Damage) on both or either engine. There is a tendency of small stones/debris getting sucked into the engine. Maintenance of turbo props are more labor intensive than jets. A jet engine is less complicated to work on and much easier to maintain.
Now, if speed is your option, go biz jet. Turboprops are much slower but range wise, both may be evenly matched. Altitude wise, the jet has a higher service ceiling than turboprops. The higher it goes the more fuel efficient it becomes.
The most common engines used on both types are Pratt & Whitney, Garrett and Allison. Of the 3 engines Garrett is the most fuel efficient. The most proven and reliable is of course the Pratts. A few aircraft are powered by Allison but are mostly used on helicopters. These engines use kerosene based fuel called Jet A-1 as opposed to high octane fuel called AVGAS used on piston engine airplanes.
Take your pick and may I hitch a ride?