Most browsers have a "Development Tools" option that provides a number of tools including a step-through debugger similar to those in XCode/Eclipse/Visual Studio.
I personally use the development tools in Safari most of the time.
I tend to use Safari (on Mac OS) as my go to browser, so the simplest answer is probably familiarity as corresponding functionality exists in Chrome and Firefox which I've had no problems using when needed. That said, IE is not so good.
I think Chrome and/or Firefox provide more support for live editing of the current web page, however I've never made much use of that functionality.
I personally use the development tools in Safari most of the time.