Won't really make any difference. You didn't say what size monitors you're using ... but if I assume 22" displays, then at the native resolution (1680 x 1050) and 32-bit color depth, it only takes 7MB to render a display ... so each card would be using 14MB to render two displays. So even a 512MB card has 36 times as much memory as it needs for the basic display rendering ... the drivers do take advantage of this to help make window-switching faster; but that's a lot of headroom already.
As with getting a faster card, it certainly doesn't hurt anything to go with the 1GB card ... but I doubt you'd notice any difference in real-life performance.
As a real-world example, a few months ago I switched out the card in my main system (the one I'm using now) from a 512MB 2600XT to a 1GB nVidia 9600GT -- just "because" (the sale price on the 9600GT was just too good to pass up). I only have two monitors (22" widescreen). I typically have 6-10 windows open, including a couple of instances with a lot of tabs in both IE and Firefox, an Excel sheet, and often an instance of Photoshop. I have noticed NO difference between the two video cards ... although I did run some benchmarks just to see how much "better" the 9600GT is => it nearly quadruples my system's score on 3DMark2006. But, like you, I'm not a gamer ... so that big improvement in 3D performance simply doesn't transfer into any real-world gains.