Alternat or desktop are the same, except that alternate is in text mode, so people with fairly exotic hardware can complete the install and, for instance, install another graphics driver.
I installed Feisty using alternate (because I am using an ATI Xpress 1250 integrated graphics processor), installed linux-restricted-modules for the kernel, and installed xorg-fglrx
So bottom line: If you cannot complete the installation using desktop, use alternate to install, and solve your problems from there