Halo 2 had an overly aggressive LOD system and the limited memory the original xbox had (64 mb).

At startup Halo 2 creates one large allocation that uses ~48.9MB of the available 64MB of RAM on the console, basically, every last page of memory they could possibly get once you account for the Xbox kernel and game executable. This region of memory is then chunked up for various subsystems in the game such as level metadata, texture, geometry, animation, and sound caches, rasterizer targets, network and simulation resources, etc.

The original Xbox had two different console types, the retail consoles that consumers would buy with 64MB of RAM, and a development console (or dev kit/debug console) that was used by game developers with 128MB of RAM. The extra RAM on the development console helped developers debug their games and run additional test code during the development process. Halo 2's E3 Demo was made with 128MB of RAM.

Halo 2 makes use of more assets and more dynamic environments than CE. They have to make tradeoffs somewhere with the limited resource pool.

Halo CE Refined mod uses the Bungie's source uncompressed 32bit textures replacing the DXT compressed versions

Halo 2 Vista and MCC use higher res source textures than Xbox retail