It depends on what you want to do with the display.
For computers, CRTs are awesome for gaming and such because of their response times. I could also imagine that they'd be pretty good for graphics/design work because of their color depth and quality. Older operating systems are especially well suited for CRTs because even high quality displays will blur the output slightly. This effect makes dithering look a lot better than on an LCD. Also, while a minor complaint, I find that the shutdown screen in Win9x only looks right on a CRT (on LCDs, the checkerboard fill pattern used to create the transparent effect flickers on all of the LCDs I've tried it on).
On the other hand, LCDs are generally better for high resolution text and office work (since there's virtually no flicker), though it's unfortunate that 5:4 4:3 LCDs died out for the most part since those aspect ratios are, IMO, the best for getting actual work done.
In the TV realm, standard def video will never look right on a modern TV. Ever. TV upscalers are generally awful and laggy, even on high-end models (my family has a lovely plasma and a samsung LED smart tv from around 2011).
HD inputs do look really nicely on an LCD TV...though that's not to say anything about the actual content that was produced in HD, however.
Based on this, I use an LCD monitor for most of my work, and I use only a CRT TV because I have no interest in HD, the DRM required to watch HD, or the actual content produced in HD.
Dual Katmai Pentium III (450 and 600MHz), 512ish MB RAM, 40 GB HDD, ATI Rage 128 | K6-2 400MHz / Pentium MMX 166, 80MB RAM, ~2GB Quantum Bigfoot, Awful integrated S3 graphics.