Denis, in general IE does not follow all web standards, so that is why it appears to be working when the other browsers are not. If the page is not looking good in Firefox that generally means the CSS is telling it do something and Firefox is doing exactly what it says. That might look incorrect, but it should just be a matter of adjusting a few things to work. I usually design for Firefox (or Safari/Chrome) first since I know those are standards compliant browsers. Then I test in IE, and in general that will look fine too since the code has been made standards compliant from the start.
I would recommend approaching your page in steps. First, use sculptor to make a page and verify it looks good. Adjust any of the CSS as needed to get the page working good first and foremost. Then add a menu to your page. Using the built in presets, these should look pretty good together. Once you start modifying the menu, do just one thing at a time and test. If it starts to break, you will then know exactly what setting is causing the problem and you can try another approach.
The tools are designed to work out of the box, true, but they also allow full customization and just like anything with CSS, that can introduce browser issues. The presets for both tools give a solid starting point with standard code.