Okay, I've never had a rabbit, but I've had guinea pigs, and a friend with a rabbit.
First off, those cages are WAY too small for either of these animals. It's like keeping your betta in a vase. It's the norm, but it's not actually good for them.
There are cages you can make that can be any size, and will be MUCH better for your pet. :)
I'll find the link and post it for you. :)
Other than that, my friend's rabbit was pretty cool. Pink lived in a Rubbermaid box...but only while people were home. Otherwise, Pink roamed the apartment. ;) She didn't leave messes, she'd go back to her box for that, but she'd get out and scamper around while there was no-one home. We didn't know it at first because as soon as anyone came home, she'd be back in her "box" and refuse to come out on her own. We realized it because my friend lived in the apartment above the barn she managed, and we could hear *something* up there moving around. At first we thought it was something on the roof, but eventually we figured out it was Pink.
She wasn't overly friendly, not like a dog or a cat, but you could pick her up and stroke her/pet her, but overall she was just sort of a "there" type of pet. Nothing negative about her, she didn't bite or anything, but she wasn't terribly interactive either.
My guinea pigs were rather the same way. You could pick them up and mess with them, but they'd inevitably leave terrible trails of pellets behind them...and that just grossed me out. So, I left them in their box most of the time. They were kind of cute though, they'd stand up for food and scoot around and be excited when I'd put a new shoe box in there, things like that. And they'd talk when they wanted food. I'd take them outside sometimes and let them roam around in the grass in a little enclosure, things like that.
Keep in mind though, they may live FAR longer than you think they will. I adopted both of my Pigs through a guinea pig rescue, and was told they were about two or three years old...and would probably only live another year or so. Try three. By the time I took one to the vet because he was starting to act puny, the vet asked me how old they were...I said I thought Rory was about five...and the vet informed me this was the oldest guinea pig he'd ever seen, and way way older than five. Those ages are just guidelines, lol! :) Bilbo lived another year and a half.