Well in theory DVI (digital) should provide a better quality picture. All those analogue adjustments (sharpness, clock phase, frequency etc) are actually fixes to correct the degraded analogue signal. With digital you don’t need to compensate for this as there is no digital > analogue conversion involved. Its just plug in and go. With digital most of the adjustments (colour, contrast, etc ) are done through the software driver.
My experience – for budget and low end LCDs it doesn’t make much difference these days – the quality of Dsub (analogue) connections have improved alot recently. And I’ve seen monitors where the DVI signal is actually worse. But for a higher end LCD it would be rude not to go with anything other than a digital connection.
To be honest though I still don’t know why analogue equiped monitors are being produced. Its yesterday’s technology and will eventually be phased out.