That's an interesting demo song in the intro. I like it. Not the typical sort of tune you'd hear from someone doing a gear review.
As far as the amps go, they sound like they're probably very squishy and wooly and fuzzy, which is typical of Bad Cat based on my experience owning a Hot Car 30R and playing a bunch of others. I mean... most of their amps were Class A, so I bet that approach to high-gain sounds has carried over to the new ones, even if Class A/B.
Their timbre is nice. They have a pleasant tonality. But they are generally pretty loose and vibey. Porcupine Tree is a good example of their higher gain sounds.