Both cars explore uncharted territory for both Lexus and Cadillac, a segment traditionally dominated previously by the 3 series coupe and now the 4 series.
Cadillac has never made a compact luxury coupe, the closest they got was the drop top Allante/ Similar to Lexus whose only experience in segment was the IS C (still partially living on under the RC). The two cars also represent two different ways of arriving at the same journey. The ATS coupe chops two doors off the sedan while sharing the same wheelbase and length, while the RC cobbles together bits from three different platforms.
As for styling I think the Lexus wins hands down. Its not that the ATS is ugly, far from it. I find the ATS to be quietly elegant, if not slightly constrained. Don't like the new badge however or the acres of legacy chrome, but thats just taste. The RC expresses its intent from the first minute you lay eyes on it, I think thats what a sports car is supposed to do, let you know exactly what it intends to be before it even turns a wheel in anger. Of course it needs to back up the talk.
I can't comment on comparable dynamics as I've not driven an ATS coupe, but we can look at the specs.
Lexus RC- $42,790
3.5L V6 307 hp, 276 lb.-ft. of torque
Cadillac ATS- $37,995
2.0T i4 272 hp, 295 lb.-ft. of torque
3.6L V6 321 hp, 275 lb.-ft.of torque.