An oenologist (a wine expert), once told me that for young wines, artificial corks (and probably screw caps) are perfectly alright. Young wines should be consumed within a year or two.
However, for aged wines, he'd stick with natural cork, because cork lets the wine breathe, letting the wine mature further inside the bottle.
The debate around synthetic is due to the fact that synthetic cork completely blocks the air. Some wine experts believe that some air is beneficial to the maturation of the wine.
Edit: The cork bottled wine benefits from a process called '[reductive aging]'. According to [WineMaker Magazine], some wines need a little extra oxygen that seeps through the cork over a long period of time.
Although cork-stoppered wines intentionally allow for miniscule amounts of oxygen to seep in over a long period of time, amounts beyond this can prevent the proper development of bottle bouquet, and proper varietal aromas can also be obscured or destroyed.
Some wines are more affected by oxygen than others (i.e., wines that are low in acidity, body, tannins, etc. -- those traits that allow a wine to age extensively). A key factor influencing the potential oxidation of a given wine is its pH level. As pH rises (i.e., or as acidity falls), the potential for a wine's oxidation increases. When pH rises the wine's phenols are in a state that fosters their reacting to each other and falling out as sediment and increasing the wine's potential for oxidation. Therefore, wines with a higher pH have lower potential for aging than wines with a lower pH.
According to Wikipedia, the benefits of screw caps in this aspect have yet to be proved.
The advent of alternative wine closures to cork, such as screw caps and synthetic corks have opened up recent discussions on the aging potential of wines sealed with these alternative closures. Currently there are no conclusive results and the topic is the subject of ongoing research. : http://www.bellavistaranch.net/aging.html : http://winemakermag.com/stories/article/indices/7-aging/55-aging-gracefully