This may be a known bug in Braid. If you take a look at this post on their official site (I realize it is from 2008, but the comments say this is still an unpatched bug), it mentions possible reasons why the game reverts to trial mode.

You can try redownloading the game, and it should recognize that you've already purchased it and unlock the full game on the new Xbox. If that doesn't work, some people have mentioned they have had success using the License Migration Tool. So you could give that a shot.

Here is a list of the command line options I could find.

Format:
"(option) (parameter)" (Description)

Language

"-language X" (Change the game language, can be one of any of the following: English, German, French, Italian, Spanish, Japanese, Korean, Chinese)

Graphic Options

"-windowed" (Run the game in windowed mode, as opposed to full-screen)

"-vsync" (Turn on Vsync)
"-no_vsync" (Force no Vsync)

"-half" (Not sure on this, I assume it graphically scales down the rendering/resolution/etc by half)
"-no_post" (No post-processing effects)

"-60fps" (Force the game to run at 60fps)
"-30fps" (Force the game to run at 30fps)
"-20fps" (Force the game to run at 20fps)
"-15fps" (Force the game to run at 15fps)

"-width X" (Specify the width resolution of the game)
"-height Y" (Specify the height resolution of the game)

Sound

"-no_music" (Turn off all music)

Level Creator/Editor

There are some other options which relate to creating content for Braid that you can read about here on the developer's blog.