If the application overrides the defaults (which is fairly common ), your changing the defaults does nothing (for that application and for the keys that might have been overridden). It sounds like Firefox overrides the defaults completely but in it's override "map" keeps some of the functionality the same as the default.

I havn't used it but this claims it will change the Firefox behaviour as well (specifically make them behave like windows for the home and end keys)

https://addons.mozilla.org/en-US/firefox/addon/keyfixer/

I think cmd-left and cmd-right are used by Firefox for " back" and "forward" so those never work on Firefox (unless perhaps you go find where Firefox specifies its key bindings and change them)