It, along with the new Ford Fusion and Mercury Milan are AWESOME new vehicles, with some of the best styling, build quality, refinement, solidity, and performance ever seen in a mostly below $30k sedan.
I wouldn't, however, consider any a true competitor to the CTS. Similar in size and style, yes, but completely different when it comes to things like the Ford's FWD vs. the Caddy's RWD, not to mention the Caddy being meant for a generally higher end segment, EVEN THOUGH, the Lincoln (and even the lower Ford and Mercury, for that matter) have arguably nicer interiors than even the top end CTS.
So, not a real competitor to the Caddy, but a group of great sedans in and of themselves--just more meant to fit with the Camry/Accord/Altima crowd.