Oh gosh, that's a classic.
I love R Lee Ermey, but either he or the producers really blew chunks on this one.
A katana does not have a 36" blade. It's usually 26-30", and a 36" blade would be an "O-Katana", which basically means "big katana".
A long sword does not have a 40-50" blade. Most longswords were under 50" for the entire sword! Even the "big boys" like the Albion Duke or Baron come in under 40" of blade length.
Chopping ICE with a sword is basically sword abuse and something that would NEVER be done with a proper sword. And you can see in the slow motion that the katana does not even cut the ice; the ice just happens to crack from the point of impact to the bottom. When the sword has made it less than 1/4 through the ice, the entire block splits and the sword just follows through.
You don't use shields with a long sword.
His cutting technique is garbage when he's cutting the cabbage, but it's cabbage, so it'll cut anyway, even with a junk stainless wall hanger blade if you really wanted to.
With the "leather foot soldier armor" (groan!), he baseball bats with the long sword. He does an actual drawing cut with the katana just by virtue of the angle he swings at, so of course it works better.
And the steel armor. Holy 18 gauge mild steel Indian made abominations, batman! He goes baseball bat with the long sword, again. He thrusts without half swording, which really makes no difference, because nobody with an ounce of sword training would thrust directly at plate; it would happen with a missed thrust that was aimed for an opening.
The katana doesn't bend as much in the thrust because it's a single edged weapon designed primarily for slashing. Only at the very end of the samurai line did they even face solid steel cuirasses, which were imports from Europe and aptly named as "pigeon breasts" (and resemble the peascod breastplates). The long sword will bend more in the thrust because it has completely different blade geometry, and it looks like they used a long sword designed primarily around slashing vs the diamond cross section of the later thrusting oriented blades.
I'm not sure what brand of swords were used for the test, but it doesn't seem like an Albion long sword, and I'm betting the katana isn't a $1,000 Paul Chen T10 Shinto either.
The video basically amounts to "let's see what kind of things we can do with a couple swords that don't reflect what they were ever used for in the first place, and decide which one is better".
I think the katana fans come primarily from either anime or the ninja/samurai movies. The katana is a highly revered object as the pinnacle of the samurai's achievements, so it has sort of a mystical "other worldly" impression on some people.
In reality, katanas were made by folding the steel repeatedly because Japan had garbage steel and it had to be folded repeatedly to remove most of the impurities. European steel was still, for the most part, a better grade of steel, and that was without folding. Japan was an isolated island for many, many centuries, and were limited to their natural resources. They did the best they could with the resources they had, and in the end, made a fantastic weapon that is *comparable* to the European long sword in it's versatility and prevalence. But just like Sir Douglas said, it's apples and oranges.
And don't get me wrong, I love katanas and have a few. I accept them for what they are, and I don't buy into the mystical nonsense that some people place around them.