Battles

Archer can target them from several kilometers away. He can also create a shield powerful enough to stop Lancer's Gae-Bolg, which is supposed to be impossible to block. Archer's Unlimited Blade Works is also possibly the only counter for Gilgamesh's Gate of Babylon. And it's already been let out that Archer is, in fact, the future self of Shiro Emiya. It's also been shown that Archer has an incredible damage soak.

Bullseye can be dodged. He has uncanny accuracy, but that doesn't mean he always hits.
 
And here's a taste of Archer.
  

@Killer_of_trolls: Bullseye technically has no superpowers. His lethal accuracy with weapons stem more from a combination of his rigorous physical conditioning and being born with excellent hand-eye coordination. 
 
@Fehafare: With the new battle conditions, the team would take scenario 1 easily since Archer's reliance on magic for the preparation of his archery would bite him in the ass as prepping regular arrows would leave him momentarily open to attack. The other two scenarios, Archer would win rather easily. For scenario 2, Archer is capable of tracing any weapons he uses for his archery rather quickly and because of the immense speed in which he can move and react to threats, he can shoot his arrows off at speeds on par with machine guns. Sure, you can give Green Arrow and Hawkeye similar speed for this match. But they lack the amount of experience at moving at such speeds as Archer regularly does. Scenario 3 would only worsen the loss of the team as Archer is now capable of summoning Noble Phantasms just about instantly while inside Unlimited Blade Works and no longer restricting Archer would allow him to dispatch his foes rather quickly.

Good fight scene here with Saber and Berserker. But really best to watch from 3:30 in.