I can't speak to the Library of Congress but from experience, the British Library has a similar system - you can preregister online or turn up in person, in which case you fill out more or less the same registration form on a terminal in the reader registration office before going through the same interview and approval process. (Worth noting in passing - the BL's interview checks you do need to use the collections, so 'get a souvenir card' probably wouldn't work there. The LoC seems to be less restrictive.)
In the BL's case, they encourage preregistration as this lets the reader order material before getting admitted - otherwise you turn up, register, and then have to wait while material is delivered to the reading room, which can take a while. I have dug around on the LoC's site for a while but can't seem to find out whether a pre-registration allows you to order material in advance. If so, this would be the major advantage.
If not... well, as the comments note, it'll save five minutes and avoid any nasty surprises when you don't have the right information to hand. (Every librarian at a major institution has stories about a researcher who flies half-way across the world to consult a vital manuscript, gets there, and discovers they need one particular piece of ID that they didn't think to bring...)