First, make sure you have the latest updates to both browsers. FireFox should update itself (if not, you can download it from Mozilla), and Safari updates using Apple Update.
Next, download the current FlashPlayer and re-install it - it will update any damaged installation in both Safari and Firefox:
http://www.adobe.com/products/flashplayer/
Finally, download and install the latest Flip4Mac, to make sure Windows Media files can play in both browsers.
http://www.microsoft.com/windows/windowsmedia/player/flip4mac.mspx
Since you said Safari works fine, there is likely something wrong with the plug-in(s) installed in FireFox.
--OD
