LCD monitors give of their best if they are running at their native resolution. That is to say that a monitor offering 1024 x 768 resolution (to pick the most common - if dated - option) will present the best resolution if the video output of the computer is running at that same setting.
What can happen - and often does in my recent observation - is that people buy a new wide screen monitor (16 x 9 ratio is common) and then find that their video options on the older computer only handle 4 x 3 ratio. This can produce a variety of effects depending on how they handle the conflict. Squashed and distorted pictures are the most often sighted results. Sometimes re-adjustment of the monitor and or video output options can produce a more acceptable result. However I still see people happily living with oval clocks and other giveaways. Some say that they even like it like that.
LCD monitors have taken over. I haven't seen a new CRT monitor on sale for a very long time now, and there are lots of perfectly good ones being dumped, or put in the back shed to make way for the new technology. I have three in this category.
regards
FoR