The major point to a laptop is portability. The major point to a desktop or tower is upgradability.
A laptop you can carry with you easily to wherever you want to go and do whatever you want, such as being able to play games on the bus (though FPS games might be a bit more difficult when the bus is moving..). As a general rule though, your available upgrades are: memory, hard drive, optical drive. The system is also generally a little more expensive for the same quality as a desktop due to needing to miniaturize, account for power consumption, and heating concerns.
A desktop has a lot more flexibility in terms of design. You can pull out the video card and put a new one in. You can add additional hard drives. You can replace the processor and the cooling system. You can change up the chassis. But it comes at its own cost: portability. Even if you have a mini-ITX system or something similar, there's then the monitor, keyboard, mouse, speakers, and such, which means you'll likely need a bag for your peripherals and then carry the machine itself separate.
The big question is, which is more important to you -- the portability factor of a laptop, or the 'modularity' of a tower? Either way you can find something reasonable for your budget.