I beat the game one XBox. You get the widebody kits after winning 11 outrun races on level 5 (after you unlock Coal Harbor West). The widebody kit is available for every single car, too. After you beat the game (beat Caleb), every widebody kit (along with everything else) is available for each car in Quick Race mode. The Celica is somehow the fastest car in the game with unique engine mods, unique ECU, and unique NOS, IIRC. The 240SX is the fastest car in the game with all Stage 3 mods and before any unique mods or tuning.
The cars I used throughout the game were:
240SX => Tiburon => RX-8 => Skyline
Surprisingly, my RX-8 is quicker than my Skyline in a drag, even when the RX-8 didn't have all Stage 3 parts and the Skyline did. The Skyline is a much better all around car though, IMO. Another sweet thing about the widebody kits is that when you convert them to carbon fiber, along with the trunk, hood, side mirrors, roof scoops, and spoiler, the entire car is carbon fiber except for the roof and pillars.
Here are some crappy cell phone pictures of my Skyline and RX-8:
