Reciprocating 4-stroke engines:
Intake
Compression
Combustion/Expansion (Power stroke)
Exhaust
Turbine engines:
Compression and intake are in the same stage
Combustion
Exhaust/Exhaust turbine
The exhaust turbines pull the excess energy out of the exhaust gas to drive the intake turbines and maybe a power shaft. The power shafts are use to either power a gear box, like on helicopters and turboprops, or they turn more fans, like on turbofan engines which comercial jets use. If there is no turboprop/turbofan, then the exhaust gas is used for propulsion, like on old turbojet engines.
Turbine engines produce constant power where as reciprocating engines only produce power on the power stroke.
A turbojet isn't necessarily better. It just depends on what you consider to be important, ie what type of flying you want to do. If you like saving fuel, flying at low altitudes, and having low maintenance costs, and don't mind being a little slower, a piston engine is the best choice, I would estimate that over 90 % of privately owned airplanes are piston powered.
On the other hand, if you like fast speeds, high altitude operation (low altitude operation is very inefficient and costly), and have the corporation picking up the fuel and maintenance bills, the turbojet wins.
Compress air
Mix with fuel
Ignite
Exhaust the expanding gases, taking energy from them.
So the answer to your question is---yes.
A turbine engine is more efficient and can operate up to 90,000 ft. a recip. can operate up to ~ 35,000 ft
The trick is in the blade design ,which it create a power full suction tunnel .