There are a number of performance differences between open-blade quadcopters and ducted fan quadcopters and they may depend on the shape of the ducts.
In theory, the most notable difference in performance is the increase in either hovering efficiency or increase in thrust. When a drone has the ideal shape of ducted fan, it could decrease battery consumption by up to 60% or almost double the thrust. However, many drones that use ducted fans don't have a duct with optimal shape or have heavy ducts and thus won't get as significant advantages.
An optimal duct for hovering would look something like this:
Also, for larger quadcopters, creating a ducted fan with tight tolerances would probably add a lot of weight which would diminish the usefulness of the duct and if a duct is severely limiting the prop size, it can limit the quadcopter's efficiency because larger props tend to be more efficient.
Another impact on performance that can be caused from using ducts, (especially for high performance or fast quadcopters), is ducts can cause the drone to react strangely when performing aerobatic maneuvers because the ducts can catch the wind and push the quadcopter off course. The ducts can also add more drag when the quadcopter moves fast. An open-blade quadcopter is generally smoother when performing fast movements or maneuvers.
In the end, If a drone has ducts with tight tolerances that don't add too much weight and has the "optimal" duct shape, it will probably be more efficient and get better flight time than a similar open-blade quadcopter but it may be less smooth and efficient when performing fast aerobatic maneuvers.
Source of information about efficiency: The ideal shape for a multirotor ducted-fan