Wolverine is a great fighter, Batman is a great fighter. Batman has great gadgets and if he had time to prepare for Wolverine he could invent some gadgets to make trouble for him. Wolverine has a military past and he has been alive for hundreds of years and he has been in many wars, he has much more experience fighting than Batman. Genetically Batman is a normal human, Wolverine is a mutant and he has healing powers and bone claws and later adamantium claws. Batman wears armour but it is questionable if it can survive Wolverine's barrage attack. Batman often has team mates that back him up as does Wolverine. Batman and Robin cannot beat the entire X Team. Professor X alone could easily subdue Batman and Robin with mind control, what Xavier might see in that bald head?
1vs1 I say Batman will beat Wolverine. I like Wolverine he was my favourite charackter in a Marvel vs Capcom video game, he is a great fighter but Batman is undoubtedly more intelligent and he has much more money available to come up with weapons to defeat Wolverine. Batman will use some kind of special weapons to incapacitate Wolverine and then Wolverine will be at his mercy. Remember Batman beat Superman!