Well, the main benefit to a DVI connection is that you get a straight digital signal from your graphics card to your monitor. An analog connection has to convert the digital to analog to cross the cable, and then convert back from analog to digital when it reaches the monitor. A TFT monitor displays its picture digitally, pixel per pixel. Via DVI the monitor gets data for each pixel, so the picture generated in the graphics card will match exact with the pixels on the panel itself. In general you'll get better quality -- but the question then remains, are your eyes good enough to notice the difference?
the good thing about dvi (it's why i got one) is -on nvidia cards- flat panel options, which lets you scale the image easily if you have a 16:9 or a 5:4 monitor and a 4:3 image
in your work pc i don't know how useful can it be, but on a gaming pc is really handy
i don't think there's quality difference with a decent vga cable