1) You usually need pay more for laptops
2) Laptops will also need to endure more wear and tear as they're mobile and will be probably be dropped or slip out of hand some time and ya need worry more about damages
3) And importantly, i think it's easier to keep an eye on what kid's are doing on a computer when it's a desktop!
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.
What grade? If still at home, definately desktop. You can build a fantastic desktop cheap, many people here would be glad to help you with picking out parts if given a budget and needs.
If its college it probably just depends on the school. If its a small school, they might not have sufficient or good computer labs on campus. But if its a university or larger college there is probably pretty decent computer labs in the buildings, and a lot of work can be done there without going back to the dorms or wherever they are going to live.
With a desktop its going to be more powerful for less $, and upgradeable. But a laptop can be taken anywhere if the student needs to work in groups outside of a campus computer lab.
"Peak?" That should be "Pique".
.I actually had that board for along time, and it served me well, but it's seriously out of date, as you know. I've given away much better machines with valid OS disks, but maybe you'll get a bite.