Firefox's superiority to Mozilla depends on what you want.
Mozilla is an application suite. It's a web browser, an email program, an HTML editor, and a few other things rolled up into one package. It's great as an all-in-one, but of course, all-in-one programs are very bloated and take forever to load.
Firefox is a bare-bones, stand-alone browser where you get to decide what you want to add via downloadable extensions. It's small, light, and quick, with zero bloat.
I personally recommend Firefox. Mozilla is slowly being phased out in favor of the stand-alone browser Firefox and the stand-alone e-mail reader Thunderbird.
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