The Katana is a superior cutting sword and arguably the finest cavalry sabre ever created. However, its superior cutting ability is not a result of the slight curve of the blade, but of the differential hardening of the blade. Differential hardening isn't a uniquely Japanese technique nor even actually Japanese in origin. The technique spread to Japan from China, where it had been developed and was already in steady use. The same technique either developed independently or was spread via trade routes in many cultures around the world as a method of solving the universal problem of unhardened steel being too soft to hold an edge well and hardened steel being too brittle to make a whole sword from.
A differentially hardened blade has a very hard edge and a softer, springier spine. That hard edge takes and holds an edge very, very well, and the softer spine soaks up the shock that might otherwise break that hard edge. However, differentially hardened blades are more likely to take a set in a bad cut, more likely to suffer fatal edge chips and cracks when striking hard objects like metal armor and may break quite a bit more easily than a spring tempered blade of similar dimensions. However, the Japanese did not have much in the way of metal armor to contend with.
A spring tempered blade is better if you're going to do a lot of blade-on-blade work, parries, static blocks, etc. and you do not want the sword to suffer from lateral torque. It will flex and return to true when put under stress, neither taking a set easily or breaking easily. If pushed too far it can and will take a set, but is still likely not to break until really pushed hard. It can be returned to true simply by back flexing it. The downside to this resiliency is that it generally will not take or keep as keen an edge as a differentially hardened sword. It may also exhibit a lot more blade wobble in use, but if you are aware of the blade's center of percussion (sweet spot) and utilize it accordingly this is not an issue.
It's a matter of trade offs. The Japanese considered a differential hardened blade to be the superior method, while the Europeans felt that a through-hardened and spring tempered blade was more reliable. Both were right, for their respective cultures and fighting styles. The natural-resource poor Japanese didn't have much metal armor so a superior cutting sword made sense against cloth and leather armor. The Europeans developed and used increasingly advanced metal armor so a sword with a brittle blade didn't make much sense to them. It's not like you can cut trough metal anyway.
