Where Opera is more secure than Firefox

Opera refuses to follow links to external protocols such as "magnet:", protecting you from occasional security holes in operating systems and programs that register protocol handlers. You can add protocols using the "Programs and paths" section of Opera's preferences dialog.

Opera defaults to opening web-page-requested new windows in new tabs instead. Unless you change this setting, this makes it impossible for sites to spoof the address bar.

Opera draws a 2-pixel border around the content area to get it an "indented" look. This makes it harder for web sites to spoof the menus and address bar.

Where Firefox is more secure than Opera

Opera is vulnerable to an attack that allows software to be installed without your permission. The attack involves getting you to click on particular part of the page. The page then pops up an executable download dialog as you are about to click. This was fixed in bug 162020 for Firefox.

Opera confusingly uses "Open" as a button label to refer to executing a downloaded executable.