Mozilla, better maybe, but safer, I don't think so. There are none of them that you can call safe. They are all being hacked.

More people use Microsoft than Mozilla, for that reason more hackers attack Microsoft than Mozilla. Also for that reason you have more people working to protect protect Microsoft. You have a greater chance of getting a hack-virus or what ever fixed fast with a Microsoft attack than you are with a Mozilla browser.

Mozilla may be better, but IE isn't bad. But Mozilla is just as vulnerable to attack.