MODX will output the same html regardless of what browser is used. The error will be down to either html/css that isn't strictly compliant between browsers.
Inspect Element in Chrome will bring up a Firebug like console where you can alter html/css on the page to see what code changes will affect.
According to this, it should work (not that that helps you):
http://www.w3schools.com/tags/tag_details.asp.
It could possibly be an issue with the DOCTYPE.
