Disclaimer
This is a personal opinion using educated though patterns. This is no way a for sure thing on who'd win or lose in a fight, as it depends on the writers and nearly any factor could come up and ruin the fight for a specific character. Keep in mind I'm also pitting them against each other one on one, their regular friends or teams do not exist during this fight unless they are used as a type of summon. I'm using Jin after the Samurai Champloo series, and I'm using Kenshin from after his fight with Shishio. Let's see who wins.
WARNING possible spoilers WARNING
While Kenshin is powerful, his fighting style involves using god like speed which is more of a super power. You can learn some moves as a normal human being, but for the grit of his moves you literally need a super power. Jin however has a fighting style that you can learn through training outside of the god like speed realm. Yes Kenshin got his powers through training, but Jin just has the better fighting style... barely.
Both Kenshin and Jin have skills, but none of them actually help in battle. So which one has more experience then? Both trained from childhood, and both of them will change up their style simply to survive and win battles. While Jin mostly survived the battles, Kenshin has won many battles using his style, and Kenshin is roughly 8 years older then Jin. This battle goes to Kenshin by a hair.
Well Kenshin wins this one hands down. Jin doesn't actually possess any super powers, while through training Kenshin has achieved god like speed to the point of wind and space manipulation. Hell Kenshin's best move is to draw his sword so quickly it literally creates a vacuumed wind blast that can hit twice if done right. Since Jin has not achieved any super powers while training, Kenshin wins this category in strides.
Kenshin's sword is a reversed bladed katana that uses blunt attacks unless he turns it around (unlikely). It isn't designed for killing. Jin has two swords and both are designed to kill. While the smaller blade is used for one attack, his main katana is still edged and used to kill people when Jin needs to. While the Reverse Blade Katana has defeated many people, it has killed no one.
Kenshin is known for not killing. That being said, while Jin's killing intent is higher, Kenshin still has a huge drive to win and has defeated opponents with higher killing intents then himself, so it is a smaller victory for Jin. Still if given the chance, Jin would easily kill Kenshin while Kenshin would never kill Jin unless Jin threatened loved ones, and even then Kenshin wouldn't kill Jin, and since this is a one on one fight, and Jin wouldn't lower himself like that, Kenshin would never kill Jin or even try.
While Jin wins in more categories, none of them put him that far ahead of Kenshin, while Kenshin's super power of god like speed kind of runs over Jin. The two would meet and if they managed to get into a fight, Kenshin and Jin would be fairly even at first, but Kenshin's skills would allow him to figure out Jin's fighting style, and his god like speed would allow him to counter nearly anything Jin would have in store. Jin would be trying to kill Kenshin yes, but Jin's killing intent wouldn't be that strong and while his sword is better suited for killing, Kenshin's weapon is still good. While Jin would be able to see some of Kenshin's moves, there is no dodging god like speed forever. Even though Jin's fighting style is a bit better, Kenshin's fighting style that utilizes the super power is still excellent allowing Kenshin to end the fight. Jin may live after the fight but after a knick out Kenshin is easily the clear winner.