On the whole, I prefer sparkling ciders. However, pairing a nice dry, full-bodied, still cider with nuts and/or a cheese plate fills a niche that many sparkling ciders would have trouble with.
Generally speaking, carbonation opens up the fruit and make the beverage seem more refreshing while still ciders tend to be a bit heavier on the palate, and emphasize the earthy tones of the apples. It's important to consider the apple blend being used when choosing to carbonate or not. To build on what gredbathurst said, carbonating can help mask lower quality cider, not all good sparkling ciders would be good still, but most good still ciders will make a good sparkling cider.
One thing to watch out for when choosing to carbonate cider is the acidity. I've had a buddy's cider that was nice and tart when still, but he carbed it pretty high (3+ vols) and the CO2 pushed it over the line in terms of pucker factor.