Ok, since the fight starts with Unlimited Blade work active then Archer wins by spamming and throwing swords at him. But, that only if he decided to fight seriously. An origin bullet at best will only tear a hole through the RM, not break it, if it did, he would have completely shattered the mercury thing. Essentially, with both range and being within the RM, Archer take it. Also, Archer has Hrunting which is homing. And, he can repeatedly fire 5 times.
But that only if he's willing to fight Kiritsugu after all this is his dad. How did he learn this? By looking at both the gun and knife, his tracing allow him to see the history of both the weapon, while he won't be able to trace the gun and I'm unsure if he's able to trace the origin knife's ability(Because origin weird). He will learn this is Kiritsugu from a timeline where he never goes to the 4th war and become a CG because of it.
He would start becoming hesitant in attacking him, possibly. He would know the danger of the knife and gun, and not come close to it. While the knife is an NP, I would think Archer--knowing the danger they possessed--would try to destroy them. While Archer will fight not to kill, the same can't be said about Assassin, who have never adopted a son.
While Assassin has Time Alter and can use it better and longer, it still poses the same risk of ******* up his body. So, he can't completely spam the thing, and the plot armour only applies if he's going to get killed and not help him kill.
So my vote would go to... really I don't know
