DISCLAIMER: I do not own Resident Evil or Marvel Comics.

The street lamp flickered. Its weak light barely illuminated the street, but it was enough to make out the man dismounting his motorcycle. He had rough dark hair, and wore a brown leather jacket over a white singlet. He looked around. He could not see anyone, but he knew someone was nearby. They stank, something like a poison.

From the rooftops, a man in a black leather coat watched Logan, his dark sunglasses occasionally becoming transparent due to the street light, and briefly exposing his blood red eyes. Albert Wesker smirked. He held up a phone, placing it against his ear.
"James Howlett, codename, Wolverine or Logan has been found. Prepare the virus samples and the adamantium restraints just in case. I'll have him back within half an hour. Dead or alive."

Wesker deactivated his phone, dropping to the ground a few metres from Wolverine. Logan turned to see Wesker. As the two locked eyes, Logan extended his claws, while Wesker pulled down his sunglasses, exposing his dark red eyes. After a brief moment of stillness, both sprang into action. Wolverine began to charge, while Wesker instantly reached Logan, kicking him onto the ground.

Wesker then tossed his sunglasses past Wolverine, before dashing up next to Wolverine and kicking him repeatedly, juggling him in the air. Wesker finally kicked Wolverine away, before pulling out his Samurai Edge pistol and shooting Logan multiple times. Wesker then caught his sunglasses and put them back on. Grunting with rage, Wolverine rose to his feet.
"Enough of this shit."

Wolverine assumed a beastlike battle stance, while Wesker positioned himself in a much neater martial arts stance, betraying years of martial arts and military training. Wolverine charged, while Wesker dashed around Wolverine, hitting him repeatedly before tossing him to the concrete. Wolverine jumped up at Wesker, but Wesker dashed past Wolverine, kicking him in the back and shooting him in the back of the head.

Logan turned and swung his claws at Wesker repeatedly, growing increasingly frustrated as Wesker evaded every strike, before Wesker suddenly slid along the ground, kicking Wolverine's feet out from under him. Wolverine hit the ground and jumped back to his feet, swinging his clawed right hand upwards, and hearing Wesker grunt with pain as the claws cut a shallow cut into his chest.

Wesker jumped away, landing on a parked car. He ground his teeth as he inspected three deep cuts from Logan's claws. Wesker glared at Logan.
"You'll pay for that!"

Wesker jumped off the car, while Wolverine charged also. The two monsters reached each other and began attacking, Wesker evading and blocking while Wolverine swung his claws like a raging animal. Wesker was confident again. Wolverine was nothing but an animal. Wesker considered himself a god over man and beast. Wesker looked forward to testing Wolverine's compatibility with the Euroboros virus.

Wesker finally gripped Wolverine's arm, swinging him around and slamming his hand through Wolverine's chest. Or at least as far as the unyielding adamantium ribcage allowed. Wolverine pulled free, gripping Wesker and pulling him into an arm lock, before swiping straight through Wesker with his claws. Wesker screamed as his body was slashed straight through, and he dropped from Logan's grip, his torso held together by a few shreds of viral matter.

Wolverine gripped Wesker's head, pulling him to his feet.
"Not so fast now, are ya, ya piece o' shit?"
Wesker began slamming his fists at blurry speeds into Logan's face, stripping flesh away and exposing the adamantium skull underneath. Any normal human would have died on the first punch, and most superhumans would have died after the first ten, but not Wolverine.
"This party's over, bub."

Wolverine gripped Wesker by the sides of the head, slamming his own forehead into Wesker's face, shattering the black sunglasses and flattening Wesker's nose. Wesker raised his fist for another hit, but Wolverine gripped Wesker's wrist, punching Wesker in the head to stagger him, before using his claws to slash off Wesker's arm.

Wolverine tossed the horribly damaged Wesker to the concrete. Wesker began crawling away, but Wolverine followed him, working up his rage with each passing second. When Wolverine reached Wesker, the mad scientist jumped up and attacked, but Wolverine caught him, his movements now much slower. Wolverine held Wesker up by the neck.
"That's checkmate, Wesker!"

Wolverine tossed Wesker up into the air, sweeping the claws of both his hands through Wesker, vivisecting the self-proclaimed god. Wolverine walked away from the pile of parts that had been Wesker. He wiped the infected blood off his claws before retracting them, and then sat on his motorcycle, riding away.

Reasons for this outcome:

1. Wesker's weapons are his hand and his gun, and obviously these weapons are not adequate to kill Wolverine, as Wolverine's adamantium skeleton has been proven almost indestructible on more than one occasion, and Wesker's hand is only ever seen going through a missile shell and the hull of a plane, neither of which is even bullet proof. Wolverine takes hits from the Hulk, and Wesker's strength was proven to not even compare to the Hulk when Chris and Sheva were shown to actually be able to grapple him. If Chris tried to grapple Hulk, he'd be lucky if his arms were still attached afterwards. Wolverine's claws, on the other hand, would definitely cut through Wesker. Sheva's knife was shown to cut through his flesh but not his bone, but if his bones were anything like Wolverine's adamantium ones the missiles would never have gone through him as they did when Chris and Sheva killed him at the end of RE5. It was implied that direct hits from armour piercing missiles would indeed penetrate Wesker's body, which would explain why he caught the missiles fired at him apart from the ones that killed him at the end.

2. Wesker is faster than Logan, thus allowing him to control the fight for the first few minutes, and their strength is arguably comparable, but there is no denying that Wolverine's durability would keep him going more than long enough, and Wolverine's fighting instincts would eventually get the better of Wesker's martial arts style attacks, especially with his claws damaging Wesker over time.

3. Wesker is a very capable fighter, but it is obvious that Wolverine's battle experience is far superior, as he faces superhumans all the time, while Wesker is used to killing humans. Wesker would also become relatively predictable once Wolverine knew his fighting style. Wolverine is arguably the better fighter in terms of skill. Wesker's technique may seem better, but if his skill was so great, he would have stopped every attempt made by Chris and Sheva to grapple him, such as when Sheva flipped him over using a wrestling move.