Contrary to what Andrew states, I played LSW on the xbox in widescreen. It is either impossible or I can't figure out how to play it widescreen on the 360. Black bars down the sides.
Just to be clear, I don't know if LSW supports widescreen or not. I've never played it and and I was just describing the general behavior of the 360.
Based on what you're describing, it doesn't sound as if Lego Star Wars is a widescreen game. If you played it widescreen on an Xbox, you were probably outputting a 480i/p signal to your TV and the TV was stretching the image. If you want to do this on the 360, go in to the display settings and set your preferred resolution to 480p. This will cause the 360 to stop formatting the video for a HD/widescreen aspect ratio.