In order to talk about potential strategies, I think some important questions have to be answered: does Master Chief have all of his weapons on him, around him, on call (like Pelican drops), or are his selections more limited? Does he have access to vehicles? Because, as far as we know Doomguy doesn't really do vehicles. Does Doomguy have access to those sentry bots from Doom 3? Are there other living things in the area he could use to power the Soul Cube and the Artifact (I'm assuming the Artifact has at least one use off the bat since it's not a weapon), or can he just use it in the fight without having to charge it with kills?
If Chief has all of his weapons one, the fight is really close, because he has a friggin enormous arsenal. Doomguy still has a slight edge, imo, just because I don't think anything Chief has quite matches the Gauss Cannon (especially with Siege Mode), Turre-Mode Minigun, or, of course, the BFG for raw, death-dealing power. However, Chief probably does have the edge in utility. Another question: Does Doomguy have the Doom (2016) weapons and gear from the multiplayer, like the Vortex rifle or personal teleporter? Because if he doesn't, he doesn't really have a good long-range answer to Chief's sniping weapons (though Doomguy would be all about closing distance anyway) and if he does then he has some extremely deadly tools to work with. If Chief doesn't have his weapons on him, that could be a problem, because he'd have to be able to get to them, which Doomguy could make extremely difficult, even if they're called in by Pelican drop.
If Chief has vehicle support, I think it's pretty clearly a stomp for him. Same goes if Doomguy has a Soul Cube fully charged to start with; I don't think the Bubble Shield would stop it since, at least in the lore as I understand it, part of the reason it works so well is that it reads more like a living thing than a weapon, so it would more than likely just go right through the shield and puree a very surprised Chief. If there are things there for Doomguy to kill, and charge the Cube and artifact for multiple uses, well...it's going to be very hard for Chief to counter that except by killing them first, which he could do, but would open himself up to Doomguy to do it, giving Doomguy an advantage either way.
Another question: does Doomguy have any runes from Doom 4? Does he get infinite ammo until he's damaged a certain amount, or can he stun his enemies by hurting them enough? That could give him an extra bit of help too. Most of the runes wouldn't be huge, but the runes for infinite ammo, boosting his equipment (like grenades), and especially the rune for getting killed once means he doesn't actually die the first time it happens could really give him a huge advantage. I still say Doomguy regardless, unless the answer to "Does Master Chief have vehicles" is "Yes" and Doomguy doesn't have a fully charged Soul Cube, but depending on the answers to those other questions the difficulty of the fight and the number of times Doomguy wins out of 100 changes drastically, imo.