They look so damn similar, from the style and color of their armor down to their behavioral traits. Seems like Bungie simply saw the success that Doom had over their Marathon series and thought to themselves “you know what our next game needs? A massively overpowered super soldier in green high tech armor who spouts sarcastic one liners in the face of an overwhelming alien invasion” and went to town with that concept. And it worked like a charm, they cranked out six massively successful games before id/Bethesda decided it was time to reboot the Doom franchise 2016.
Perhaps it was payback for them to give Doomguy the Crucible in the reboot games (which looks a lot like the energy sword from Halo), but I can’t help but think these two are essentially the same character.
Early video game copyright history was also a lot more loosy goosie. Bethesda cut its teeth on Terminator licensed games, because no one really cared about video games and corporations would give away licensing rights for a song.
If you look at early gaming history, there’s a lot of stuff that wouldn’t fly today copyright wise. (Iirc Nethack has enemies from Tron, folks very happily made and distributed Star Trek fan games - heck, in the early 00’s you could buy unofficial mod packs for video games in stores.)