in short, portable hdds can be carried anywhere without a power brick. less space than desktop hdds, but more convenient if you're on the go and can deal with say 80-160gb. also only runs at 5400RPM as opposed to desktop's 7200RPM+. not really noticeable when you're just transferring stuff. generally only usb (2.0)
desktop hdds hold much more (250GB to over TB), can have more options as to connecting to computer (firewire, usb, and/or eSata). also runs beyond 5400RPM (generally 7200RPM) power brick means you need wall outlet. powerful, fast, less convenient.