I would say that you want to compare HD (high def) CRTs (cathode ray tubes) to Plama displays. Not SD (standard def) CRTs.
SD CRTs do provide better black levels and can provide a cleaner picture on SD material, but don't offer the same resolution for things like DVDs and better programming that plasmas can. So blacks and shadows may be better on a SD CRT, the image won't be up to the same resolution as the plasma.
But, on a HD CRT vs. a plasma... The CRT will have better blacks, greater shadow detail, and do a bang up job handling pretty much everything thrown at it. If I were buying, and had space for, a rear projection television I would likely go with CRT over anything. If 34" (or so) was all I needed for a TV then I would go with a CRT. But, we have a tiny living room and the plasma stays. At 50" I would have to go rear projection which puts me on a large CRT, smaller LCD/DLP or my plasma. Plasma works very nice for what it is as long as you remember what it isn't.