Hearing tree limbs breaking would definitely be a heart stopping experience in any dwelling. Here in Texas we don't have the gargantuan trees that you have but they can still do tremendous damage if they land on your house or car.
I'm in tornado alley but right on the edge of it so we don't get as many sleepless nights as someone living right in the middle of it. We definitely get some prayer inducing weather a few times a year, though.
Sometimes you have to just sit on the couch and pray ;~D
The barn is a much more substantial structure, with huge beams. I think sometimes it would be the safer palce to ride out storms ;~D