A combination of ido-mode and dired make it incredibly fast to go through the directory structure of any project. It's also really easy to open a shell wherever i am visiting at the moment--including remote directories!--which I've found incredibly useful.
Once I'm in a file, there are a whole ton of movement commands in Emacs that make teleporting around natural. Just one example that seems hard to duplicate in an IDE is the mark: in the course of normal editing, you often set the mark to do things like highlight regions of code. Then, later on, you can cycle back through your old marks, which takes you back through the parts of the file that you were active in. It's like bookmarking a line in the file, except much more lightweight--it happens in the natural flow of working on a file. This is just one example of many very productive features.
Another great example is rgrep. This command lets you search through files in a directory. However, the really cool thing is how it displays the results: you get the filename and the line where the match happened. You can go to the file directly or actually edit it in place in the rgrep results buffer! It's very nice for certain tasks.
Really, Emacs is full of incredibly well thought-out productivity boosters for everything you will do while managing software.
Moreover, it is not limited to language agnostic things. If your want Eclipse-like Java support, you can have it with eclim, which actually uses Eclipse as its backend. I also know of great IDE-like support not based on Eclipse for all sorts of languages from Python through OCaml.
Now, Emacs does have a learning curve. It will take a bit of effort to get good with it. It will probably require changing your entire workflow to take advantage of all the awesomeness. But it's more than worth the time investment: getting comfortable with Emacs is an O(1) action where the benefits it confers are a significant O(n) (if not better!) bonus. The more you program, the more you'll gain.
Learning Emacs gives you significant gains even if most of your job involves browsing around and editing existing code.