INDOOR HOUSE RABBIT -
PROS: Rabbits are social but quiet creatures. When you take them into your home, they feel like they belong somewhere. Like they are part of a family, just like in the wild. Indoor house rabbits generally get more company, even if it's just a little kid talking outside it's cage. They are also very cleanly and can be taught to use a litter box. Because of this, indoor rabbits also get more exercise. Rabbits do live longer if they have time to stretch their legs and do their little hops and skips, even just a couple times a week.
OUTSIDE RABBIT -
PROS: When the rabbit sheds, or molts, the hair stays relatively outside, as does the hay. If you have allergies to rabbits, you may be able to still have one by keeping it outside.
CONS: Rabbits are social creatures. If you are not able to provide him with daily interaction, he may become fearful and antisocial if he's left alone. You also have to go outside every day, whether raining, snowing or shining, to feed and water your rabbit.
So there you have it. Personally I would choose a house rabbit over having a rabbit outside. Of course, if I could have my rabbitry indoors, I would. Instead, since our house can't facilitate a 10-hole rabbitry max, I'm going to be getting a shed very soon.