Well, this is where we can start to see how bad TVs really are for your eyes
Your standard, cheapo, everyday kinda TV shows a resolution of 640x480. Also, the way the guns are designed and the tubes are used, the image shaves a whole lot and kinda preforms a form of antialiasing for you. On your comp, most TV tuners are designed for 640x480 as well, or a tad higher. Unfortunetly, most of us don;t have our resolutions at that level, so you WILL notice that the image appears to be fuzzier because you're used to seeing the image on a TV, although it's technically the same image, well more or less anyways.
I have my PSX and DC hooked up to my Radeon VIVO and Santa Cruz and I love it. The PSX looks pretty bad, but the DC looks almost as sharp as on the TV. If anyone can explain to me how that works, I'd be glad to listen!