Well.......There's This.......
Probably the biggest problems with laptops is, they get stolen. My feeling is if you can get away with the desktop, do it. Your inquiry doesn't take into account, whether or not the child actually needs a computer in the classroom with him or her. This is why many schools are issuing laptops to their students. If you can pull your work off a machine at school, and transport it to home with a USB drive, I wouldn't even consider a laptop. Obviously you need to be more familiar with your school's IT landscape to make an informed decision.
As I said earlier, laptops get stolen. We receive numerous requests, attached to numerous "reasons", (some very creative), as to why people want to install a different operating system, remove BIOS passwords, or reformat hard drives associated with netbooks or laptops, than for other types of assistance with these products. I'm fairly certain that many, many of these entreaties are not on the up and up.
Something else to consider is, what school, what grade, and the child's general sense of responsibility before you decide.
Remember, if you go the desktop route, you get damned near twice the computing power, for half the price.