Both Firefox and Chrome allow you to save your passwords directly in the browser. It seems like a handy little feature. However, neither are terribly secure methods for storing passwords.
Chrome doesn’t password protect your stored passwords. All one needs to have access to all your passwords is to access your Google account. This isn’t a problem if you are the only one using a particular device. However if you login to other devices besides your own and forget to log out, you give the next person who logs in access to not just your Google account but to all your passwords as well. This makes it a less than ideal tool for password storage.
Firefox allows you to set a master password to keep your stored passwords safe. However, it uses less than ideal measures to keep the master password from being hacked. This makes saving passwords in Firefox rather an insecure option for your password storage.
What is safe? In truth, no method of password storage is completely safe except for memorization. However, your best bet is still a third party password manager. Regardless of which one you choose, they all give your passwords adequate security. Best of all they generate strong and effective passwords for you so you only have to be creative once.