Ok, I have Blaise and Sophie. Sophie brought home a couple of pet candidates before I relented and let her have that wheezy fox. Blaise has never brought anything home. Sophie regularly asks for allowance, Blaise has asked once. When I come home, Sophie comes running to greet me about 10 times more often than Blaise.

What I am asking is, is this pretty normal? What are your experiences with your children? Is this just the difference between boys and girls, or is it just randomness with the AI?

I have two girls and what you described is how my kids act too... The first child Runa I adopted seems to have all the dailog and interacts with me more then the second child does. I was thinking that maybe it is because when I adopted Runa she was a only child for a while in my game then I finally broke down and adopted the girl from Whiterun and again she kinda just hangs out but Runa does all the cool stuff and says all the dialogs etc..