RobWard,
I will attempt a (partial) answer your question.
1. A fan usually has a higher pressure ratio across its face than a propeller, and a fan often has more blades.
2. A fan and shroud unit will have a smaller overall diameter than an ordinary airplane propeller for a given horsepower, mostly because the shrouded fan blades have a higher and more uniform loading along their span.
3. A ducted fan will be quieter for a given power level; because sideline noise, which is the worst part of a fan's or propeller's noise signature, is largely captured by the shroud.
4. A ducted fan usually runs at higher rpm than a bare propeller, which helps to make the ducted fan a good match for a high speed engine.
5. Static and low speed thrust for a ducted fan are typically higher than for a bare propeller at a given power level, because pressures induced on the shroud by the fan flowfield add to the thrust. However, the static and low speed thrust advantage of the ducted fan is lost if its diameter is too small.
The thrust of an ordinary propeller at low speeds (under 50 knots)is generally poor. Ultralights could gain both thrust and noise benefits from a well designed ducted fan, if the weight can be kept low - a major challenge.
6. At higher speeds (above ~100 knots, depending on the details of the overall fan & duct design, the duct drag exceeds the duct thrust gain.
7. Duct weight is considerable, because the low internal and leading edge pressures can result in very high loads.
8. The weight and high speed drag penalties are the main reasons you don't often see ducted fans, except on jets.
9. Jet engines with bypass fans always use ducts, despite the weight and drag penalties. Ducted fans are not essential for fanjets, however. Douglas Aircraft did tests on a DC-9 with "unducted fan" engines. Their fan blades were fewer in number and larger in diameter than the fan blades on an equivalent ducted fanjet engine. The unducted fan engine was a somewhat more efficient propulsion system; but it had noise issues. (On a typical fanjet engine, the duct helps contain the fan noise, plus the fan duct exhaust is mixed with the core jet exhaust to reduce jet noise as well. The unducted fan can do neither of these.) There may also have been certification issues due to extreme unbalanced forces resulting from loss of a large fan blade.