Since when do the X-Men have general psi-blocking tech? They didn't use it when they've gone up against Shadow King, White Queen, Exodus, Apocalypse, Cassandra Nova, and numerous other telepathic opponents. Beast finding a way to mess up Phoenix one time doesn't prove they can stop any telepathic opponent, and all those examples suggest just the opposite.
Magneto's helmet isn't lying around the X-Mansion (not that you said it was), so that's only marginally relevant. And Magneto creating psi-blocking doesn't prove it's easy to do -- he's a genius who's created whole high-tech bases seemingly from scratch. Joseph, the Magneto clone, created a way to suppress Rogue's personality absorption, which Xavier couldn't do after years of study. And as Ahura pointed out he probably didn't make psi-blockers in a day anyway. (Plus, Magneto's psi-resistance has also been attributed to everything from force of will to latent telepathy.)
Anyway, I just don't like the idea of assuming someone can whip up a way to largely neutralize their opponent's main power just because they're smart and invent stuff. We were too permissive with the psi-blockers in previous seasons. It'd be different if your guys had actually built anti-telepathy tech in less than a day before, or if the X-Men really did use anti-telepathy tech as part of their standard aresenal. (They do have a telepathy-proof room -- I used it in my writeup, in fact -- but there's no reason to think it could be converted to something someone could carry around with them, especially in only 24 hours time.)
That said -- I agree that Flash could get a bunch of attacks in before the telepaths could think the thoughts to stop him -- he's that fast, and they only think at the speed of thought. But I'm not sure he could take them down before they thought the thoughts they'd need to stop him. Cable, probably, if he can phase through his telekinetic shields. (Assuming Cable isn't telepathically levitating a mile above the battlefield where Flash can't find him or get to him, and attacking Flash telepathically from there -- which I think he could do.) But can Flash really take down the totally indestructible Juggernaut before he can think one thought? It'd only take one thought for Xavier to knock him out with a mind blast -- at least if I don't buy the psi-blocking tech.
I also question whether Flash can freeze the Juggernaut if Juggernaut is already charging forward at the start of the battle (which would be a sensible thing to do if he knows about Flash's speed draining). Juggernaut has an infinite momentum power where once he's moving he can't be stopped. Even Thor's God-Blast couldn't exactly stop him, just caused the earth to give way beneath him. Not that being able to charge forward in a straight line matters much. I just thought I'd mention it.
Regular/Medium battles I could see going either way -- both sides had some good arguments.
Short version: I don't buy the psi-blockers, and without them Juggernaut needs one attack to beat Flash. While I agree Flash gets in a lot of attacks before Juggernaut gets in one, I'm skeptical that he could take him down before Juggernaut gets in the one attack. I see that as the key battle.
So I vote the Immortals. Good writeup and debate by both sides, though.