What are the advantages and disadvantages of ducted fans in designs such as the Airbus E-Fan?
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Advantages of ducted fans would be:


reduced noise
Better containment of broken blades
protection of ground personnel when the engine is running
Smaller size than a comparable propeller
They look like a fancy jet engine. This is probably the main motivation of Airbus for their use on the E-Fan.


For almost all aircraft designers, their drawbacks have weighed more heavily:


Less efficiency, because a smaller mass of air is used for propulsion
Additional friction drag and weight from the shroud


The highest propulsion efficiency is possible with a large, slow-spinning prop. Once flight speeds approach the speed of sound, the propeller has to become smaller to avoid supersonic propeller tips, and then the shrouded design becomes more attractive. Electric airplanes so far are not fast enough to profit from this effect. I would be very skeptical of the increased thrust claim - both efficiency and thrust of the E-Fan ducted fans are lower than what a well-designed propeller can offer.

The addition of the shroud only increases thrust when compared to the naked fan, but the fan is a poor replacement for a decent propeller at low speed.