This is yet another example of why it's better to be a monarchy.
When Dubya shows up with soliders/children/aircraft carriers as backdrops, it's blatantly partisan. He has no real interest in them, just in their political value.
In contrast, when the GG does things with children, there is no political purpose. She's there for the children--in her official capacity, to be sure--but still there as an expression of caring.
How much better to have a head of state that can represent your country without having a political motive behind it?
God save the Queen.