When I say a CRT softens the image I don't really mean it looks out of focus. In fact CRT screens are great at making it seem like you're seeing a lot of detail.
The person I originally replied to used the terms "blurry and soft," which is what you get when something is out of focus, such as when the focus pot on a CRT's flyback transformer is out of adjustment. Here's a picture of a Star Trek TOS DVD playing on my 32" CRT TV:
Sharp / in focus, and that's with an RF connection, which I prefer to use because I am going for the NTSC TV broadcast look (and a signal from an NTSC RF modulator is literally an NTSC TV broadcast, just a very low-powered one). My TV also has composite video, S-video, and component video (YPbPr) inputs, the latter of which would give the highest quality picture with a DVD, since DVDs are encoded with digital component video (YCbCr) to begin with.
This is the effect I'm talking about. The screen's gotten rid of all those nasty MPEG compression artefacts like magic, but the runabout landing pad has disappeared too.
Yes, CRTs are great for improving the look of poor quality video sources. Did you take those two pictures? If so, what are the details of each one?
Though if my VHS tapes are any indication of the quality of the signal coming down the wires, then TVs weren't being given much detail to lose:
VHS (240-250 TVL) isn't full NTSC broadcast quality. Betacam SP (~330 TVL) is approximately NTSC broadcast quality, and was the de facto standard TV broadcast format for many years (it was never a consumer format, unlike the completely different Betamax format, which was about 250 TVL like VHS HQ), including the years that TNG was in production. LaserDisc (~425 TVL) exceeds NTSC broadcast quality, and DVD (TVL doesn't really apply because it's a digital format, but in analog terms it would be 540 TVL) exceeds it even further.
Even though Betacam SP is NTSC broadcast quality on paper, in practice, it adds a certain "flavor" of its own to the picture, and you get better results from an NTSC broadcast by using a higher quality source, such as LaserDisc or, especially, DVD. Anything higher quality than DVD is completely wasted on an NTSC broadcast though.
Also, keep in mind that not all CRT TVs were created equal, not even when talking about the standard-resolution (~15 kHz) consumer ones. Some of them could display significantly more detail than others. When I was a kid in the 1980s it was mostly the high-end ones from the big Japanese companies (e.g., Sony, Mitsubishi) that could do that, but by the end of the CRT era in the mid 2000s, even most mid-tier ones (like my 32" RCA) were producing very good pictures by ~15 kHz standards.