the best reason i can think of in using a console controller with a pc adapter is the ability to use the actual console hardware with your setup. examples include dreamcast, xbox, and playstation 2 consoles.
as for being better or worse than a normal pc usb controller, it is very difficult to make generalizations without talking about specific controllers and adapters. there is a plethora of usb pc controllers available, with MANY resembling playstation/playstation 2 controllers. xbox controllers are actually usb pc controllers. i have heard of driver problems with certain psx>usb adapters but i have also heard of ones that can use the gerneric HID windows drivers.
so it really boils down to what you want to do and how far you want to go. you can get a good "dual shock"-looking pc usb controller and use it to play all sorts of console emulators. its a tried and true layout and lends itself well to console games. if you want a "more" genuine experience, you could use the actual console controllers on your pc, or even get more genuine and play the games on the actual console. now, you either need an adapter or hack the pad which can get you in all sorts of driver problems with a pc.
people who hack psx digital pads and buy usb adapters solely to avoid using a keyboard encoder in their mame setup make absolutely no sense to me..