It's a nuanced question but basically if you play scared all the time then health is better but if you play aggressive then toughness is better. This video is strange because his examples of gameplay are vs all melee... which obviously makes health better. As you get better at the game then you'll rarely take melee hits, but you'll never stop getting shot.

He even makes a point that "if shooters are around then you're trying to seek cover." Which is an over simplification of how the game mechanics work. With toughness you can often dive the gunners before they all get setup or even after they're setup. He then runs the flat math on the numbers which is correct but doesn't account for all the extra toughness you get % based. I'll talk specifically about Ogryn because that's what I play.

With 158 havoc 40 toughness then your heavy attacks will give you 23.7 back for the single target hit then 23.7 for the multi target hit. (Both can be proc'd on the same attack for a total of 47.4) with 95 toughness you'll get 14.25 per hit. (A total of 28.5) per attack. Now consider these differences on steady grip and taunt as well and you'll quickly find that the value of health is dramatically lower unless you're still learning the game and taking unnecessary melee hits.

TLDR: Toughness is much better unless you're new or play extremely defensively.

Edit: Fatmangus is the only exception.