When talking about airplane engines the big questions are thrust vs weight and efficiency bands. Propeller engines have a relatively low thrust to weight ratio. This means for the weight of the engine it doesn’t produce much thrust. That being said they produce more thrust at lower engine speeds than a jet would. So a propeller engine consumes less fuel at low speeds than a jet would.
Side note: there is no real advantage to a rear facing propeller. Most airplanes that do that are gimmicks or proof of concepts for engineers. The only thing it allows is the plane can be shorter in length because you can fuse the tail section with the engine housing. But that doesn’t really do much for the function of the plane in a practical sense.
Now jets on the other hand have a high thrust to weight ratio. This means that they can create a lot of force compared to the weight they add to the aircraft. Jets are also more efficient at high engine speeds that propeller engine. This means that jets can make small things go really fast or lift heavier things than a propeller engine could, but they consume a lot of fuel to do it. Less than a propeller engine would for an equal amount of work, but a lot of fuel nonetheless.
Edit: I’ve seen a couple mentions of drones. Drones have rear push propellers for space saving and forward visibility. It doesn’t add any efficiency. While you or I may be able to see through the rapidly spinning propeller, a camera would likely catch snapshots or even be completely blocked by the rolling shutter effect. But that’s a different problem altogether. All you need to know is there is no efficiency increases, it’s merely a consequence of engineering around a plane whose main job is gathering visual intelligence.
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