Fiddler and Firebug are two different tools that we use to solve two different problems.
Firebug is primarily used to Inspect / Tweak the DOM, script debugging, and basic network information. It primarily deals with things inside the browser.
Fiddler goes much further underneath of it. Fiddler is useful for inspecting network / protocol level information that the browser is doing, as well has a lot of analysis helpers.We typically use this when We are trying to diagnose compression issues, see network traffic, very fine grained details for timing, or making your own requests to the server, which we do when we are tinkering with SOAP / Web Services.