Not sure about the local statement. My vr has problems as I drive away from my house, and wifi data disappears. 3 seconds later it works again when my non wifi data connection firms up.
I actually test to see how quietly spoken, quickly (running words together), and in heavy wind noise it will work. And am amazed how well it deals with it. The visual shows a series of mistakes and then it corrects itself, showing it understands not just the sounds I make but the context in which they make sense.
Found this note on StackOverflow. "From what I can establish, Google tests the availability of a connection prior to deciding whether to use offline or online recognition. If a connection is available initially but is lost prior to the response, Google will supply a connection error, it won’t fall-back to offline."
While it works offline, I bet it doesn't work as well. For the vast majority of use (set alarm, launch known program, etc), local should be ok. But when doing complex dictation, I ASSUME online (with deep context analysis) would have an edge.