With the guitar turned full up, the Classic Fuzz in the Axe FXIII sounds just like a real Fuzz Face. (I have several original Fuzz Faces from the 60's.) I compared it directly to my Roger Mayer Classic Fuzz and it sounded exactly like it, but it does not react the same as a guitar plugged into a real one. Especially when turning down your guitar. That is probably why Dweezil Zappa uses quite a few fuzz pedals before he goes into the front of his Axe FX.
I definitely prefer plugging my guitar straight into my Roger Mayer Classic Fuzz over just using the Fuzz Face (Classic Fuzz) in the Axe FXIII, because of how a it reacts when turning the guitar volume control down.
I like a germanium Fuzz Face for some things and silicon Fuzz Face for others. Both are good, but sound different.
If I had to choose one, I like the Germanium the best.
The Benson in the video clip sounds really good, but it does not sound like a fuzz face to me. I would not use that as a comparison.