According to the journal Poultry Science, go with the cardboard. The packaging may not change the way the eggs taste or change their cholesterol levels, but it does make a difference in getting them home without cracking.
Researchers at Clemson University in South Carolina compared the two types of packaging. The cardboard had a 4.6 percent breakage rate, while the plastic had a breakage rate of 12.6 percent.
And in case you wondered why you have to take move every egg in the carton to check for breakage, it's because 55 percent of the cracks are at the egg's bottom. You'd miss that if you just opened the carton top and looked in.