The double pole version disconnects both the Live and Neutral from the socket outlet, whereas the single pole version disconnects the Live only (provided that the socket is wired correctly).
One advantage of the double pole version is that if it has been wired with Live and Neutral transposed, the Live will still be switched.
I am not aware of any application requiring double pole switching on a socket outlet (sockets are available unswitched).
When working on any mains electrical item, you should always unplug it, rather than rely on a socket switch.