Hi
It may be due to the anti-aliasing and sub pixel rendering that OS X uses. You can select which font smoothing style to use and switch it off for fonts below a certain point size via one of the system preferences (Appearance?).
An ADC to DVI adapter should give you a better picture quality overall as you'd be using a digital rather than an analogue signal (assuming the monitor accepts a digital DVI input). They're relatively cheap to buy, although don't confuse them with the DVI to ADC adapter (that you mentioned) which is much more expensive and converts the other way around. You need to convert an ADC port into a DVI port.
Ironically if you've just switched from a CRT, it's probably the sharpness of the LCD that's allowed you to notice the pixelisation. It's probably always been there, but because CRTs tend to blur the pixels together, you've probably never noticed.