What is the setting for this battle? Would make a big difference considering Bradley's Ultimate Eye.
Round 1: Bradley, with difficulty. Assuming both have no knowledge of one another, Logan should at least be fast enough in reaction speed to keep up with the Fuhrer and the Ultimate Eye would allow Bradley to evade Wolverine's attacks. The things that would drag this match out would be James' regenerative abilities (decapitation is Bradley's only means of winning here) and any possible environmental obstacles (depending on setting which really needs to be clarified here as obstructions give Wolverine a possible chance to strike Bradley with the Ultimate Eye obstructed).
Round 2: Wolverine would ultimately take this by outlasting Bradley. Bradley would still overwhelm James in attacking, but Wolverine's adamantium skeleton and regenerative factor would prevent any means of attack in Bradley's arsenal from offing him. And no Cerus, adamantium can't cut through other objects made of adamantium. Adamantium is nigh-invulnerable to attack as such where depending on how it is made, either only high-level hax could affect it (true) or those with a high level of superhuman strength [like say, Hulk or Thor] would be capable of damaging it (secondary).
Round 3: Bradley wins in most scenarios. Without his regenerative abilities, Wolverine would likely bleed to death from the wounds he sustains from Bradley's sword attacks and the Ultimate Eye would still make it very difficult for him to land attacks.