I think they have their own personalities and they can vary enormously. I had one rabbit that was basically wild and didn't like humans. It liked next doors dog though. And I had another that seemed to think it was a dog, actually enjoyed human attention and would come and find us- on his own terms, of course! The first time I saw my dad cry was when a nasty fox got him when he was 9- we were all devastated as he was such a character.
I'd say they are good pets for older children who appreciate their nature and how they live in the wild. As others said they do not like picking up, although they might like coming up to you for a pet if you're sat around. If your children are the kind that are just happy to watch them hopping about, and come up to them when it feels like it, rather than something that will play with them then rabbits would probably be ok. The positive aspect of their disposition is that your kids won't get a crazy bunny seeking them out to attack, as a cat or dog might do. They only tend to bite if picked up and scared.
They do take a lot of looking after, and a lot of space. They need daily (I'd say at least twice daily really) attention. They need things to play with, and lots and lots and lots of hay. You can still get hefty vets bills. If you let them in your house they LOVE biting cables and they can zone in on the bloody things like some kind of bunny ninja, bite through them, and scarper off to hide before they get rumbled.
I don't know if cats are too much of a risk once they are big. The cats stayed out of our garden when we had rabbits. Mainly because rabbit-who-thought-he-was-a-dog would try and shag them
I'm only letting mine free range when I'm in the garden this time as I don't want a repeat of the fox incident.
I've got kids and I've given into the demand for pets because I'm sick of my son infesting my house with woodlice/snails/newts as 'pets'. I'm getting rabbits as they are the only pet that I'm personally happy to look after and I know that I am going to be the one doing nearly everything, if not everything. They are my favourite animal- they are vegetarian like me, aren't in your face all the time demanding strokes like dogs are, their poo isn't disgusting like dogs, and I'm allergic to cats. We also have a mahoo-sive garden and I'm shit at gardening. We're hopefully getting 2 rabbits from a rescue- advantage being you kind of know their temperament. I am spending a small fortune housing them in a massive wendy house- aviary set up…cheap they ain't.
So…I'd get them if YOU want them and want to look after them, and have the capacity to do so. Which is what I expect anyone would say about a pet.