The benefits of having your rabbits out longer would probably be:
1. Better Health
2. Better socialization (handling/petting)
3. When rabbits use enough energy, they are calm and sweet. When they are rowdy, it is near opposite.
The disadvantages
1. Safety (This isn't a problem if you have your rabbit in a controlled play pen indoors with no wires or other chewable things that are unsafe such as plastic)
2. Mess (note: pee can be cleaned up fairly easily and most litter trained rabbits don't have a problem with accidents)
If you have a larger cage for your rabbit you can get away with not having them out for a long period of time, but it's still nice to do. For example: my rabbit's cage is 24inches wide, 24 inches tall, and 48 inches long, a fairly nice sized cage if you ask me. I also have plenty of toys in there for him to entertain himself. But I still keep his cage open nearly all day. He is a very sweet rabbit and his health state is great. The only problems I have with him now are him chewing my carpet, but it's easily fixed by moving him or giving him a new toy to distract him.
As you can see, you can't really have your rabbit out for too long and I would say to get a play pen, attatch it SECURELY to their cage, and let him/her choose when it's play time, and when it's nap time. :bunnyheart