According to a posting from Xbox Live’s Major Nelson any Xbox 360 S users who purchased the Xbox 360 Gears of War 3 Limited Edition Console must purchase a special transfer cable to move data between two Xbox 360 S (also known as the Slim) consoles.
Xbox 360 S to Xbox 360 S Transfer Cable
Apparently this is only an issue between two Slim consoles and the regular data transfer cable should work just fine to move data from a standard Xbox 360 to the Xbox 360 Gears of War 3 Limited Edition Console. Of course another option is to manually re-download all your content from Xbox Live by going through your purchase history. A tedious process but costs you time instead of money.
Instructions on how to do a data transfer, no matter which cable your using, are available at How to use the Xbox 360 transfer cable at the Xbox.com website.