The fact is that the larger ships are more vulnerable to windage. They're stacking so many containers so high that these ships are quite vulnerable to losing their centre of gravity, if you will, in the wind. They're also vulnerable to high seas. A long ship in a high sea can suffer structural stress that can impair its integrity, so no, the bigger ships aren't giving rise to more safety.
The additional safety equipment they have on board could give rise to more safety if they felt that they needed to be more careful, but because they're not liable for their judgments of seamanship under the international convention, they're not more careful. They're simply responding to the economic drivers that caused them to want to bring more cargo more quickly.