Of course Carbon is a modern OS X API, and if you're trying to create C++ programs, it's the easiest API to use. Apple may initially have intended it to be some sort of portability layer, but it continues to be updated, and Apple themselves write major parts of OS X and iApps in it, from the Finder to iTunes.
I'm not saying I wouldn't like it in Cocoa, but it's a stretch to call it "deprecated" or imply that it would be better to use X11 than Carbon.