I want to add on to what I said before.
Granted, the stallions at the farm my horse is boarded at are overall sweet as apple pie, but I wouldn't advocate having one as a family horse no matter how well-trained and gelding-like they are. Take this farm's boys for example (I'm excluding the mini stallions at this time, so I'm only talking about the four Andalusians). They're all complete dreams in their fields. Walk right up to you for pets and rubs and the occasional treat, you can walk into their field to just hang out or take them for whatever you need them for. When they know it's time to work (cute shows for kids) they can be ridden together in the same arena, even next to each other. In their stalls they're good buddies, but I wouldn't trust them out in a field with each other or other horses.
With people they are quiet sweethearts in their stalls (except the youngest one who has a habit of thinking biting is an acceptable play thing to do...nope, smack). Like all animals, they are unpredictable. Stallions, IMHO, are moreso than geldings in some respects. One day it was raining so the horses had to stay inside. They were restless, but they had plenty of hay to munch on. I was doing the oldest stallion's stall and he decided to bust out and trot up and down the stallion aisle trying to bite through the metal stall grating. I was injured (caught between him and the wall), but didn't notice until after I rounded him back up in his own stall. Hormones can be scary, I'll say that. Sure, any horse could do that. But I think stallions are more prone to thinking with their hormones than most geldings.