Pitting these two historical warriors is really baffling.
Tactically, on one on one fight, where no follow up combat will take place (i.e. simple duel) the samurai will win.
In a campaign where large scale battles will take place, the spartan has an edge in their phalanx formation. If the samurai (generally a cavalry unit fighting on horseback) can break the phalanx, they(samurai) can win. If they cannot, the spartans will still be alive to hold their ground.
This could result in a battle of attrition. No matter how skilled an army is, casualties will mount. It is the speed where you can replace your losses that will count. The Katana takes several months to make and the samurai takes years to be trained. The spartans however, being trained as a warrior since birth, can draw up manpower as replacement almost immediately. Their weapons can also be manufactured faster than the samurais'.
Logistically, a large scale battle will favor the spartans.