This will quite honestly depend on your video card, monitor, and monitor cable. The thing with analog vs. digital is digital is all or nothing. If the signal arrives, its perfect. If it doesn't there's no picture. There's no in between. For this reason, arguments about cable quality, etc, are all silliness in the digital realm unless you are talking long cable runs. You either get the picture, or you don't. Analog on the other hand is by definition sucseptible to any variety of effects. Bad cables, interferance in the signal, bad analog output, bad input on the monitor, and so on.
In general, a GOOD analog connection should be just as good as a digital connection - *technically* the digital is perhaps a bit better, but its generally not perceptible. Analog also has the benefit of being more adjustable on most monitors. But start introducing some x-factors, and the analog quality can go down. Neither of my monitors has DVI at current, and the picture quality is excellent. But depending on your individual situation and components, you could have different results. You won't really know till you try it.