The transport, digital blocks aside, one very important thing in many of the best CD players (and DACs) is the quality of the analog portion and the power supply.
If you take two players with identical DACs and transports (not uncommon these days), and give one an excellent power supply and analog stage, and the other gets a typical SMPS and single-chip output (if even that), the former, I would submit, would sound noticeably better than the latter. Blu-ray players would usually fall into the latter category. Good CD players will often have very good power supplies with excellent analog output stages.
With some exceptions, BRD players are not designed to be good CD players, and rightly so. Often, the requirements for excellent audio are at odds with the goals of such players. And those BRD players that do, incidentally, perform well with CDDA are quite expensive ($1000 or more), and in my own experience, merely equal the audio performance of a mid-range dedicated CD player. You get a mid-range CD player bolted into what is, inherently, a Blu-ray player.