Seeing vs hearing is a red herring.
What really matters is whether information about one child being a girl fixes a particular child. It doesn't matter how the child is fixed (a popular variation is "I have two chilren and the older one is a girl"), but it does matter that out of the two children, it is now known about a specific one of them that it is a girl. In that case, out of 4 possibilities, 2 are ruled out, and the answer is 1/2.
If all that is known is that one of the children is a girl, only one possibility out of 4 is ruled out, and the answer is 2/3.