The sad part (well, one of the sad parts) is that the Florida case, as I recall, was only discovered after the death of one of the children. Like the NZ case mentioned by Primaflora, the switch was discovered when one of the girls needed treatment for a serious heart condition, that led to her death. During the testing, her doctors realized she could not be related to either of her parents.
This must be very heartbreaking for both families. One set of parents has lost their child, and it must seem like a miracle when suddenly they discover they have another child. The other parents are also grieving for a child they never knew, and are worried about losing the child they raised.
The best case scenario would be the avuncular relationship MandaJO described. In the most positive case, there could be many benefits – an only child might discover siblings, you would have the relief that each child will receive better medical care because the doctors will know the family’s medical history, two sets of doting grandparents instead of one.
If this wouldn’t be TOO WEIRD, and it might be, I would want to involve any siblings as much as possible. It would be easier (I think) on a child who suddenly had to visit his “new” family if his brother was also going. This makes it seem more like a visit than being ripped from your home. Also, instead of switching the two children for 4 weeks every summer, both children would spend 4 weeks together with family A, and then 4 weeks together with family B. This could be more like gaining a sibling than becoming a changling. Of course, this is all on the premise that I think the other family is at least somewhat normal.
I don’t have children, so I tend to agree with Arnold on the bonding thing. The earlier the switch is detected, the easier it would be to let go of one baby. Personally, I would still like to have some contact with the other family, regardless of who gets which child. I can also see how one family might like to foster a long-term relationship, while the other family might take a “let’s move on with our lives and forget about this” attitude. It’s hard to say whose view would take precedence, it’s not like there’s a compromise. Well, “some contact” might be a compromise between the commune idea and no contact, but there’s no compromise between some contact and no contact.
If I ever have a switched baby, I hope the other parents are Dopers, that would seem to make things a lot easier. 