The original Mozilla was a suite of applications that included an HTML editor (Kompozer), a mail client (Thunderbird), a PIM (Sunrise), a browser (Firefox, although I think it was called Navigator or Firebird back then), and a chat client (Chatzilla). It was lot to load.
When Firefox was first released as a standalone browser, Microsoft's thralls immediately started whining about the size of it, as if nobody knew that 90% of IE was already loaded and hidden from sight. When you open IE, you're basically just loading the GUI front end, so it looks small in the process manager. Fact is, it's huge, and Windows won't even operate without many of its components running, since they comprise the bulk of the file manager. An OS without a file manager is like an airplane without engines. Impressive, but useless.
Today, everybody but IE is pretty fast, with the differences between them being noticeable only on benchmarks rather than by the seat of your pants. It mostly has to do with the Javascript interpreter, and as I understand it Google's Chrome is currently leading, at least by the numbers. In reality, I'm not sure you'd notice any difference. The downside to Chrome is the EULA, which gives Google way too much leeway to play on your computer and watch what you're doing, so I don't use it. It's MY computer, not Google's, and what I do with it is my business, not theirs.