Okay, so first, let's rehash what's been hashed. The two swords, symbolic of the warrior (Bushi) class, might be better viewed along the lines of a military officer's sidearm. Warriors used a whole range of weapons and may have had specialties in the spear or the bow as primary weapons.
In examining the Japanese blade, whether the tachi or the katana, in terms of blade geometry, efficacy must be determined within the context of the times.
Combat - combat, tactics, strategies and the technology of war is not static. The desire for superior weapons and ways to employ them against an enemy continues to this day with emergent technologies used to get the “upper-hand”. An interesting turn of phrase in itself. Why is the upper hand considered an advantage?
Seriously though you can’t divorce how a weapon was employed from the war culture to which it was adapted.
The reputation of the katana was inflated to mythical levels by the Japanese militarists marching towards war. The icon took on super and unfounded characteristics and the propaganda remains embedded in some folks attitudes to this day.
Now consider a country with poor natural resources and at war with itself for almost a millennia. They invented a process of steel making that made exceptional blades for the purposes of their environment that were nothing less than pure genius. The blade was flexible, yet stiff enough for slicing. The blade was durable with a hardened edge that could be repolished. It was a great compromise between competing and contradictory needs.
Then there’s the artistry that would evolve. Damascus blade making was also lost to history and then re-invented and the skills that went into making this fine steel and again the artistry in the blade and the sword furniture leads one to ask if the craftspeople of today can do what the craftspeople of the time could do skills-wise? Not just in something like inlay, but in creating the themes, not just replicating them. Bouncing back to Japanese blades, you would be hard pressed to find the same craftsmanship today in the making of sword furniture as you could during Muromachi Jidai.
In answering your question and again pardon the pun as i don’t want to put to fine a point on it, the question can’t really be answered in a blade geometry by blade geometry matrix and today’s silly tv comparisons assume to many things that are lost to history including the skill sets of the original warriors that used these weapons.
In it’s time and place each blade was suitable for it’s task. Think in terms of “combative Darwinism” - as technology and tactics improved, weapons changed to face the new realities or battles and wars were lost. Even the Japanese warrior came to understand that the sword was not mightier than the bullet.