If you're a story completionist, Lara's Shadow is the most essential piece, as it officially "ties up the ending in a nice little bow".
The DLC consists of two primary story packs and several smaller outfit additions: Tomb Raider: Underworld ISO & XEX DLC - XBOX ...
“Hardcore fans will warm to Lara's Shadow in a way that they probably didn't with the rather disappointing Beneath the Ashes .” Eurogamer.net · 17 years ago If you're a story completionist, Lara's Shadow is
Reviews of these expansions are mixed, often balancing the thrill of new content against its short duration. Pros: Polished and fun
“ Beneath the Ashes is a relaxing stroll for veterans of the series and a fun one at that... Pros: Polished and fun. Cons: Too short and easy.” Console Monster · 17 years ago
Xbox-exclusive content is a unique chapter in the franchise's history. While the base game launched on multiple platforms, Xbox 360 owners received two critical story expansions that actually provide the "true" conclusion to the trilogy started in Legend . DLC Overview: The Missing Chapters