Desktop pluses - can upgrade many components easily and sometimes repair broken components. Easier to upgrade to a high end graphic or gaming machine. Less expensive for the same computing power
Cons - Sometimes noisy depending on fan
Laptop pluses - portable, can be moved from room to room or taken anywhere. If you don't need a screaming temple of doom machine, easy to get a computer that will suit your needs. Can easily add a keyboard or monitor when the computer will be generally staying in the same place. Handy to take to meetings or other events where you need to share information or take notes.
Cons - hard to upgrade or repair
Get it quick cause you won't be able to get XP much longer!