For those registered, this Quora page has a balanced explanation of the pros and cons of CD vis-a-vis vinyl.
etc.
Here's the engineering perspective in a nutshell:
Human range of hearing extends from 20Hz - 20,000Hz (note 1);
The sampling rate for CDs is sufficient to fully capture sound in this range;
Digital samples allow for perfect recovery of the original analog signal when properly decoded (via the NyquistShannon sampling theorem ) (note 2);
The Dynamic Range (difference between loud and soft sounds) capabilities of CD audio are greater than that of LP records.
Now, here's where things get tricky. The above paragraph is a big "if", because the mastering processes -- those steps that are taken to move the master recording to the final product -- for LPs and CDs are inherently different, and these processes can result in significantly different-sounding recordings.
As a result many CDs out there are actually worse recordings (for one reason or another) than their LP counterparts. But note that this is not a function of the technology but the way it has been used (and abused).
etc.