From watching British television, at least, I gather that "Brilliant!" usually is akin to American "Cool!" or "That's great!". On the other hand, in the US we would use "brilliant" to describe Albert Einstein (or someone else who is exceptionally intelligent).

I think there's a bit of a nuanced difference in how we use the word "clever" as well. Where you would call someone clever, we would usually say he is smart (or maybe brilliant, if smart enough). "Clever" in the US often has a slightly derogatory sense to it. Someone who is good at solving a Rubik's cube is clever. Yes, it takes a certain intelligence but of a gimmicky sort.

I think the American version is inherently sarcastic.