How did jet engine aircraft perform compared to the best reciprocating engine aircraft during WW2?
Much longer take-off distance and less endurance, but higher speed at all altitudes with jets. The performance advantage of jets widened with increasing altitude and resulted in a higher service ceiling. Both the Me-262 and the Ar-234 would fly at least 100 km/h faster than any propeller airplane, and the Ar-234 could fly reconnaissance missions over France and England in complete impunity. A Me-262 test variant (262 V9) with a low-profile canopy reached 600 MPH in level flight.

This gave jets the possibility to break off combat at will. They could only be engaged with success when they were flying in for a landing with empty tanks or by chance, when the jet pilot was unaware of his opponent. Since the Me-262 was designed to intercept bomber formations, it was not suited for dogfights. The Heinkel He-280, on the other hand, was evaluated in 1943 against a FW-190 and would easily outturn the propeller aircraft, so this was not an engine-related characteristic.

Note that the first kill of a Me-262 was by a de Havilland Mosquito, a very fast propeller aircraft that could outrun almost all other propeller aircraft of its time.