Making sure things are cross browser compatible is always a challenge. But a general rule of thumb is you should just avoid using padding in your CSS. It’s probably the #1 reason you’ll get cross browser issues.
Avoid using padding in general. It especially causes issues when you need to set a width in your CSS because you’ll get different results in IE and Firefox. The better method is to put a div inside a div (called an inner tube) and set margin on the inner div.