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.