Laptop vs. Desktop
First off, there's the price/performance ratio. Whether you're spending $300 or $3,000, you will get a more powerful computer for your money if you're willing to give up portability.
You have more upgrade options with a desktop. Most laptops will let you easily add RAM and swap out the hard drive. But your average desktop can take more RAM than your average laptop. And with a desktop's multiple bays, your drive options open up considerably. For instance, you don't have to choose between an SSD and a hard drive on a laptop; you can have both. Upgrading a CPU or graphics card--reasonably easy tasks on a desktop--are difficult to impossible (usually impossible) on a laptop.
Which brings up the issue of repair. It's easy to open up a desktop PC, check to make sure the cables are secure, clean out the dust, remove a broken part, and replace it with something generic. Laptop repair takes considerable skill, and many parts are specific to that model.
On the other hand, laptops are portable. That's a very good reason to buy one. They also use less electricity.