So propeller engines are more efficient than jet engines? Is this true regardless of speed, plane size? I always thought jet engines were revolutionary, were they really just quieter?
Yes, propeller based engines are much more efficient. They don't waste quite as much energy "throwing" air out the back. It is generally true regardless of size. However, using a propeller does limit the speed of the plane. In fact, an airliner with an open-rotor engine (like the one described in the article) will most likely fly just a bit slower (around Mach 0.75-0.8 instead of 0.85 like most airliners today). The propeller becomes very inefficient when shocks start to form on it. Therefore, you have limitations in how fast you can spin the blades and how fast you can fly. You eventually reach a speed where the blades cannot generate any more thrust to keep accelerating the aircraft.
Jet engines were revolutionary, but not because they are quieter. Pure jet engines are actually incredibly loud. The only way the noise was reduced in modern airline engines was the advent of high bypass engines where most of the air going through the engine is only slightly accelerated.
Another thought. I heard that putting a duct around a prop gives you more thrust ceteris paribus. Is this just not true, or maybe only true for slow speeds?
Yes, it is generally true. There is not a big dependence on flight speed because the inlet on jet engines slows down the flow before it enters the engine. So even though an airliner might be flying at Mach 0.85, the face of the engine only sees about Mach 0.3. The reason the duct improves the thrust of the engine is because it reduces the pressure losses (improves efficiency). A fan (or any stage in the engine compressor) increases the pressure of the air. Since air moves from high pressure to lower pressure, the air that you just pressurized wants to sneak back around to the front of the fan around the tips. By putting a duct around the fan, you help keep air from sneaking back and robbing you of the work that you just did on it. In fact, the efficiency that you gain is highly dependent on the clearances between the duct and the tip of the fan. A lot of work goes into reducing these clearances as much as possible. You can imagine that that is a non-trivial task since the parts of the engine expand and contract based on temperature, and also vibrate and have dynamic structural behavior.
That was certainly a big part of it. Jet engines, although revolutionary, were developed only about 40 years after heavier-than-air flight began. It's hard to group all jet engines into a single category and discuss trends of the entire group. One grouping you could make is the distinction between turbojets (and very low bypass turbofans) and medium/high bypass turbofan engines. With turbojet engines (like the original designs starting from the 1940s), you had the ability to produce a lot of thrust at the expense of fuel consumption. These are the types of engines that you had in military jets and supersonic planes like the Concorde.
However, for modern airliners, fuel consumption is important. So a second class of jet engines was used that send a small portion of the air through the "core" of the engine, where it is burned and power is extracted, and the majority of the air is accelerated through the fan without being combusted. This is much more efficient (and much quieter, since most of the noise you hear is from the interaction of the high speed air coming out of the engine with the surroundings). The open-rotor concept described in this article is just a natural extension of the high-bypass engine. You get a much more efficient engine when you can increase the ratio between the amount of air that you accelerate through the fan compared to how much you send through the core and burn (this is called the bypass ratio). Since the weight and drag penalty increase exponentially as you increase the size of your engine, removing the duct around the fan becomes necessary once you get to very large bypass ratios.
