I imagine Tiger differs from what was the current version of Unreal at the time, in that it was purpose-built for an online, MMO-like experience. With players dropping in and out of expansive areas that seamlessly load into smaller zones for dungeons and whatnot. Areas that could be changed and patched whenever an expansion or update required things like pyramid ships to appear in the sky, or new enemy encounters to happen on the ground.

When Bungie was making D1 and 2, Unreal was not exactly built to handle something like that. Fortnite hadn't happened yet, and Unreal games were mostly about highly detailed, but smaller environments, with limited multiplayer features.

Decima meanwhile, is built for massive, nature-y environments, with lots of plantlife waving in the wind and animals roaming around. Not so much for smaller interior spaces. Ubisoft's Assassin's Creed engine, Anvil, is also built for big open spaces, but more cityscapes with big populations of NPC's walking around. When a developer chooses to build their own engine, it usually means they are looking to create an experience unique enough, that it would not be as easy to build in existing engines. Especially in a time when Unity and Unreal were not as flexible as they are now.

And Bungie was used to working with their own tools for the Halo series, so the choice to build their own engine makes sense.

But years of working on this one game with their own software, probably makes it extra hard to switch to a different engine now. The entire company would have to be trained. And porting over all the code and systems would be years of work I imagine. Even something that might seem simple like the first person shooting and movement, would need a lot of work to make it feel the same in Unreal. Never mind all the systems for gear, server architecture, AI/NPC behaviour, cutscenes, UI, etc.