Old World wines are lighter-bodied, lower in alcohol, and brighter acidity. They show more earth-driven flavors.
New World wines are fuller-bodied, higher in alcohol, lower acidity. They are more ripe on the palate.
Some things to note: the line between the two differentiators is fading.
Climate change is pushing the Alcohol percentage in old world wines up and causing the grapes to be more ripe. Changes in the wine industry is causing new world Vignerons to find higher elevation sites to grow grapes which lead to higher acidity and lower their ABV. Reference: Old World vs. New World explanation