Firefox 42+ has a Tracking Protection feature that is enabled by default in Private Browsing mode. Firefox can show a shield icon at the left end of the location/address bar that some content is blocked by Tracking Protection, click the shield icon for more information.

You can disable this feature in "Options/Preferences -> Privacy" or via the about:privatebrowsing page that get when you open a New Private Window.

• Options/Preferences -> Privacy: "Use Tracking Protection in Private Windows"

• https://support.mozilla.org/en-US/kb/tracking-protection-firefox
• https://support.mozilla.org/en-US/kb/control-center-site-privacy-and-security-firefox

You can set this pref to true on the about:config page to see more Tracking Protection choices in "Options/Preferences -> Privacy".

• privacy.trackingprotection.ui.enabled

You can open the about:config page via the location/address bar. You can accept the warning and click "I accept the risk!" to continue.

• http://kb.mozillazine.org/about:config

Robzere said

I cannot access my bank using Private Browsing, but can access WITHOUT using Private Browsing. This is obviously not secure.

When you say "this is obviously not secure" I am not sure what you mean. Firefox's private browsing mode uses temporary storage, so any history of your private session, and any cookies set by websites in your private session, disappear once your close the last private window.

But otherwise, private browsing windows are not more secure than regular browsing windows — unless some content is being blocked. As cor-el mentioned, the Tracking Protection feature blocks some content. This sometimes creates problems with the site not working, however, and in those cases you may need to unblock (using the shield icon described in "What happened to Tracking Protection?").