The CAT amps are arguably the most powerful tube amps ever made ("powerful" in the sense of their wattage ratings being almost meaningless -- they can drive virtually any speaker to loud levels cleanly). They also do finesse, especially the all point-to-point wired $50K limited edition monoblocks with the outrageous 55 lb. output transformers. The newer models with circuit boards aren't chopped liver either.
The only downside is that they could be less finicky about requiring only the most carefully vetted output tubes, and when tubes blow, they take out resistors, which, given their outrageous weight (192 lbs. each for the limited edition monoblocks), makes owning them an obsessive's pastime (the comparison to Ferrari's best before those cars became reasonably reliable is not off the mark).
In short, while BAT makes a very fine product, the CAT amps are an extreme product that is without peer in my experience.