The Xbox Classic version isn't just a "lite" port; it actually has features the original PC version lacked:
Unlike the original PC release where you had to swap between a gun and a flashlight, the Xbox version allowed for more atmospheric tension by keeping the lighting engine’s shadows sharp even on limited hardware. Exclusive Features
To fit the massive PC game onto the Xbox's 64MB of RAM, the developers had to get creative. DOOM 3 [Xbox Classic]
The large levels from the PC were broken into smaller chunks with more frequent loading screens to manage memory.
A dedicated two-player cooperative campaign was added, allowing players to fight through the Mars research facility together via System Link or Xbox Live. The Xbox Classic version isn't just a "lite"
The original "flashlight vs. weapon" mechanic was intact, which many argue is essential to the game's survival-horror identity.
Character models and environments were simplified, but high-resolution normal maps were used to keep the "bumpy," detailed look of the PC version. Character models and environments were simplified
This version famously came in a steel book and included full ports of Ultimate Doom and Doom II , making it the ultimate "Doom box" for the time. Legacy and Impact