I love the Mega Man franchise. I loved Azure Striker Gunvolt.
Zero wins this decisively. In physicals (durability, speed, reflexes, strength), he outclasses Gunvolt. There is no larger discrepancy between the two than stamina. Zero is capable of mantaining terrifying combat power indefinitely, whereas Gunvolt (unassisted by Lumen) is severly limited and quickly burns through septimal energy, even with technological upgrades. If he overheats, it leaves him completely open (no prevasion, Flash Field defense or attack, no double jumps or air dashing). Zero suffers none of these drawbacks.
For Gunvolt to do any significant damage to Zero with his Flash Field, he must first "tag" Zero with one of his projectile weapons, which will be incredibly difficult due to Zero's agility and his ability to cut or reflect projectiles (not to mention Zero's Shadow Dash which allows him to phase through enemies and attacks). If Gunvolt were somehow able to tag Zero, and he activates the Flash Field to attack, he'd leave himself open to Zero's deadly saber combo counterattacks, since Gunvolt's prevasion ability cannot function with the Flash Field active. The Flash Field will also not be useful as a defense as it cannot stop energy projectiles or attacks, which happen to be the majority attacks favored by Zero.
There is the possibility that Gunvolt might open up with Luxcaliber or Voltaic Chains, but Zero could tank these. After all, he's taken multiple lightning bolts from Harpuia as well as Panther Flauclaws's 100,000,000 volt shock and kept going. Or Zero might just Shadow Dash through Gunvolt's big attacks.
As things stood in ASG, without the power of Lumen, I don't see Gunvolt lasting very long against Zero. And if Lumen buffs Gunvolt with her Anthem ability, it remains to be seen if they could overcome Awakened Zero, since again, he drastically overpowers them with that rapid fire, instant kill, Genmurei Zero as well as his complete invulnerability.