In terms of character, I'll let Wikipedia do the work;
Mugen, is, in many ways a player character to the bone.
He is interested in showcasing his strength and little else. This demonstration of physical prowess isn't necessarily limited to just swordsmanship though. When there is a contest for eating, he joins. When there is a graffiti contest, he joins in. When there is a baseball game against Americans, he wins it. When not being able to read becomes something his comrades are able to harass him about, he learns it. In this, he is much like Guts of the manga Berserk in some of the early material. His goal is to find strong enemies so that he himself may become stronger.
His adventuring spirit though, isn't just killing. It's living life the way he wants to. He has no use or need for social conventions. He's perfectly happy fighting against lawmen as well as bandits. This allows him to be put into many situations that a paladin or other good type of character would inherently avoid.
Jin on the other hand, like Usagi Yojimbo from the graphic novels and comics, suffers a bit because he's a true believer of the samurai caste and its meanings. Because of this, and the fact that the lands are now at peace, the true value of armed men is diminishing and doing so rapidly. Who needs a standing army of soldiers when there is no war? This theme of a soldier without a war is used often when dealing with Samurai in films such as Hari Kari, an old classic of soldiers out of luck and needing support to comics such as the already mentioned Usagi Yojimbo.
It's one of the reasons why having characters active in a time of danger, in a time of trouble, is often more viable. There are things to do when the country is at war and when times are tough. When things are good, its time for another type of character such as yakuza or nobles or rising merchants. For a warrior, things are difficult in these times because they're not needed nor wanted.
Jin finds himself fighting against what he sees as the corruption of the samurai spirit starting from the first episode, asking if its worth serving a corrupt lord when service is part of the samurai creed, but to do so to those who are foolish or greedy or otherwise unworthy of that service, renders that need to serve false. It is why he walks the road alone as opposed to being the head of his own school.
The two are an interesting contrast in many ways.
The former, a wild fighter looking only to test his strength, and the later willing to walk the line of Bushido even when its inconvenient to do so.
The show has several other bits going for it that a GM might want to crib for his own game.
For one, there is a showdown between Jin and a blind assassin. The battle takes place on a narrow wooden bridge. This prevents a lot of movement and fancy footwork. The environment becomes its own thing.
On another showdown between Mugen and an assassin, they fight on a boat. The small boat capsizes and puts the battle underwater. Try to keep some options available for those scenes where it needs to be dramatic and needs to move fast paced.
In terms of pacing, while the series does follow an overall goal of finding a specific individual, most of the episodes are very self contained. This type of campaign would be an easy model for a GM to run with an over arching goal and various encounters that the GM puts together between sessions to keep things moving along.
Samurai Champloo does mix a lot of modernismsbling or having other aspects of 'gangsta' life hit the points of let default setting that 4e uses.
Samurai Champloo is worth a viewing and Netflix has it for those with that service.