Twinkie - My rabbit is a house rabbit. He's never been outside, in fact, if we leave the back door open he point blank refuses to go out!
It just depends what he's used to. I would say they would get more bored outside! At least in the house there is the general bustle of people.
I'm a big softie.... and after his paralysis... I'd bring him indoors.
However, all the other rabbits I've had have been outdoors and a few never liked the house even just for a run about.