A few reasons I listed on the video description...
Blood spatter is glitched out on BFG while its fully present on xbox 1
Gunfire no longer lights up the environment on BFG, fully present on Xbox 1
Imp fireballs no longer cast shadows on BFG, casts shadows on Xbox 1
Plasma gun's blue light no longer casts on the gun and environment in BFG, works fine on Xbox 1
Much less bullet hole decals from the shotgun on walls in BFG than on Xbox 1
Cutscenes on BFG Edition are cropped from the 4:3 original, Xbox 1 are true 16:9
1:30 of the video you'll notice the main character's shadow is completely glitched out on BFG Edition
Obviously the textures, resolution and level size are better in BFG and the PC original, but so many other details are worse in the BFG Edition than both the Xbox 1 version and the 2004 PC original.