Logan Needs his healing factor to move around. The Adamantium Bonded to his Bones is Rather heavy. The reason He doesn't get winded by walking 5-6 feet, is because His stamina is increased to superhuman levels through His Healing factor.
If wolverine Doesn't have his healing factor The adamantium bound to his skeleton would be lethal, as was shown in all The Previous experiments of weapon x.
But I'll ignore that to let the battle continue.
The difference in speed between The battousai and logan is tremendous. While Wolverine is peak human, Kenshin far exceeds that in both travel and reaction speeds
While the battousai can't Cut through adamantium, He doesn't have to. There are several points He can strike (eyes, Throat, in between the ribs etc, that will kill him and avoid the bone.)
@rein: ok, assuming his body can handle his skeleton without problems. although for someone who is at least 100 years old, i think he'd have learned some moves against fast opponents. im vouching for Kenshin, but wolverine can nullify a lot of the blade with his claws, which cant be cut, and a well timed unsheath can knock the blade from kenshin's hands...