I don't know anything about Eden's zero tbh, but looking at Homura's profile it looks like Guts has a pretty hefty skill, versatility, and experience advantage.
He's incredibly intelligent and creative in battle, and always thinks of inventive ways to defeat physically stronger and larger opponents, though with the Berserker Armor a lot of that is replaced with sheer anger and bloodlust; however, even then he's incredibly skilled and quick on his feet. (Depending on whether or not Schierke's support is allowed, he can even maintain more control over himself without suffering the mental drawbacks of the armor)
I'm not sure if his Probability manipulation will factor in much here, but it's also there I guess. Could help him dodge a few deadly attacks with enough luck I suppose.
With the Berserker Armor activated, he'll fight until his last drop of blood is spilled, and even without it his endurance and pain tolerance will make him insanely hard to put down. There's also the Berserker Armor "repairing" him.
His Acrobatic abilities, agility, and skill are boosted through the roof with the armor as well. He has pretty decent tricks up his sleeve as well like Analytical prediction and his tools such as bombs, crossbow bolts, and of course his arm canon (which she definitely won't see coming, since it's hidden by the armor).
Guts can also deal damage to her soul with his hits, and honestly the AP advantage won't be that big once he activates the armor, so his versatility and skill should shine through.
He can also mostly shrug off electrical attacks as we've seen with Ganishka, so her lightning attacks shouldn't really do much damage. Or at least nothing that'll decide the battle.
Also I'm not sure if it's allowed to give him support from his party in the form of Puck's Elf Dust (healing) and Schierke helping him maintain control, but either way it shouldn't sway the outcome very much.
I'd say I give this one to Guts.
