Robin Hood and his templars win this fight very easily. They have one key element that the Samurai don't and that is personal shields.
The Templars are also better protected by their armor. The Samurai may have a slight edge in agility with their light weight armor but a full body suit of plate armor made from tempered steel is actually very maneuverable. It does need to be noted, however that, Japanese plate is not significantly lighter than European Plate armor and is definitely not nearly as durable. The Samurai also lack chain-mail which was often quite effective at gurading against thrust attacks. Although, i don't think armor will be THE deciding factor in this fight, the Europeans definitely have the advantage especially considering that the Katana dulls very quickly and easily. The fact still remains though, both the Japanese and European armor were susceptible to direct sword thrusts from a trained warrior. As a few people have already noted, the Samurai armor was designed primarily to defend against arrows and spears. This is crucial when considering that the Templars tempered steel plate was designed primarily to defend sword combat and was also quite effective against arrows.
Now if we look at weaponry, i'm sure most people will be quick to say that the Katana is in a league of it's own of sharpness and true this may. The Katanas strength comes from slashing or slicing, not piercing and referring back to armor, the Europeans plate armor is renowned for resisting the cutting of blades. The Katana, in weight and aerodynamics, is certainly going to be a faster weapon to use. This, however shouldn't discount the agility that the Templars swords offer. Not knowing exactly which sword the Templars are using here makes it a bit harder to deliberate but most of their swords were all made to be swift and used in one hand alongside of of the shield. Also, despite what many people may believe, Katanas do not cut through swords.
I'm also more inclined to give Robins archers the edge, under his training, for obvious on screen feats.
As for which leader is a better open field tactician, i think is irrelevant here. We do not know the type of experience that Robin had in open field battles. Although, if one insists that, Katsamoto gets the edge, i suppose i couldn't argue that sufficiently because under King George, Robin is obviously incredibly experienced in battle and war theory and even though King George engaged in open field battle often he most known for sieges.
For me, the deciding factor still comes down to the Templars shields. The Samurai were not trained to battle with shields and i'm inclined to say they would not know how to defend against other master warriors who were equally trained in extensive sword play but also trained to battle with shields.