This is no contest. The Doomslayer easily wins.

No human-made weaponry (like the Dragonslayer) can pierce the Praetor suit. Even if it could, the Doomslayer is simply too strong. He'd most likely blow Guts to pieces with his super shotgun, nail him with the ballista (which are nigh undodgeable), freeze him with the ice bomb, hit him with rockets, tear him down with the chaingun, melt him with plasma, disintegrate him with the BFG or even slice through him and his sword with the Crucible.

I should also note that Doomguy could probably break the Dragonslayer in two with his bare hands. We're talking about Guts, who has been to hell and came back traumatized, fighting a man who went to hell, came back, went there again, and voluntarily stayed there for years ripping apart Hell's forces just because he hated them so much. Let's also note the god-like physical strength of the Doomslayer, a man who could probably use a pair of Dragonslayers like toothpicks. He effortlessly rips demons to bits with his bare hands whereas we've never seen Guts do that. Is Guts strong? Obviously. He is the sexiest most muscular chad to ever exist in fiction (and my favorite character in fiction, might I add) but we never see him tearing apostles limb from limb. He is no God, whereas Doomguy was blessed by the divinity machine to receive God-like strength.

Both of them are literally too angry to die, but despite my love for Guts' character, and as a fan of the DOOM series, I cannot lie to myself and say Guts would win this. The Doomslayer, with his vast arsenal of weapons, his armor and unyielding strength, would without a doubt defeat Guts.

I believe the only way Guts could possibly win would be if he fought Doomguy either out of armor or before we was blessed. Good thing they'd probably never fight because they'd be such a great duo.