Why a Rotary Engine is More Efficient than Piston System?

Having untangling that tangled grammar...

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I assume you understand the basics of both types of engine, despite not using the term "reciprocating".

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The steam-turbine is usually designed to expand the steam through its full pressure / volume / temperature range, so from high inlet pressure to a partial vacuum in the condenser, which reverts the exhaust stem to water for feeding back to the boiler.

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The turbine's steam flow is from inlet to exhaust through steady stages, so each part of the turbine is at a constant temperature; hence low thermodynamic losses. The rotor and inter-stage stator blades are designed to give as smooth a flow as possible while extracting the maximum turning-moment in each stage. The reciprocating engine (unless of uniflow type) uses the same passages between valve and cylinder for both live (inlet) and exhaust steam, hence creates alternating steam flows with a certain amount of wasteful heat-cycling.

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The turbine is entirely rotative, so develops equivalent power from much less moving mass, avoiding inertia and vibration problems. The back-pressure created on the exhaust stroke in a reciprocating engine is minimised but some is still necessary for mechanical cushioning against the high inertia of heavy piston, piston-rod, crosshead and connecting-rod as the stroke reverses. (Although their travel is a harmonic oscillation, which lessens the inertia to some extent naturally.) However it also loses power in compressing a small amount of used steam as the valve closes to exhaust and starts to open to inlet.

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To sum up, the inertial and internal-frictional mechanical losses, and the thermodynamic losses, in a turbine are far less than in a reciprocating engine of equivalent power.