Many people are switching from Internet Explorer to alternative browsers such as Firefox and Safari. Though that might make them feel more secure, the shift has also opened new doors for bad guys.
So forget the idea that just because you've switched to a new browser, you're magically safer. You may be for a time, but to stay safe with any software, you need to keep current with fixes.
In an actual attack -- neither the Safari nor the Firefox bugs have elicited one so far -- a bad guy could take over your PC or steal your navigation history.