Why is the Priority Takeover button used?
It's been several years since I worked at United's flight training center, but if my memory serves me, it is there in case the system is receiving input that the pilot wants to exclude. As was explained to me, an example of this would be the other pilot becoming incapacitated, with their body leaning against the sidestick. In this case, one would want to use the Priority Takeover button to eliminate the other pilot's input.

In Captain Sullenberger's case, it is likely that he wanted to ensure that First Officer Skiles wasn't providing any control inputs that would work against his control inputs. 

Now, it is also my understanding that such functionality is not useful in a "hostile takeover" event, since the other pilot can also attempt a priority takeover (or use physical force, due to the close proximity of the two pilots).