Mozilla is the same thing as Firefox. If you want to be technical, Mosaic started the Browser wars. By creating the Internet Browser they paved the way for other browsers to fight by giving them a chance to figh.
I stopped using it when JavaScript broke on me in IE. Instead I now use FF. The only reason I will touch IE is to check out my site to make sure it looks good in the leading browser.
It may have happened to you before, but sometimes JavaScript just doesn't work in Internet Explorer. There is a very simple fix. Just go to Start > Run > regsvr32 jscript.dll. That repairs the jscript database. I advise to use FF instead though.