IDE ostensibly stands for "integrated development environment." AFAIK, not a single IDE is as integrated, programmable, hackable, flexible, or stable as emacs (or vim).
In Emacs, I can effortlessly open and navigate through an indefinitely large number of files. I can take advantage of myriads of language-specific modes for syntax highlighting, auto-completion, snippets, verification, prettification, truly integrated compiler/interpreter environments, you name it.
If I find I need to do some repetitious gruntwork, I can C-x ( gruntwork C-x ) it away. If this gruntwork seems excessive, I can program it into my editor and forget about it. If I find I really need some feature or functionality, I can pop open a scratch buffer, hack it, and use it instantly. No boilerplate, no compiling, no restarting.
These are just the tip of the iceberg, though. The overwhelming sense an emacs or vim user experiences, is one of power. We have complete control over our programming environment. We dictate it, hack it, and tweak it until it is effortless. This sense of power and hackability so permeates our programming environment, that it becomes physically painful to have to navigate a swarm of inconsistent modal dialogues, accept some kludges and pray they get fixed, and accept that The Developers know how best to configure our environment.