I still look in the JavaDocs. On a typical day I may hit the JavaDocs 3 or 4 times. Big deal. If I could be arsed to look it up, there's a keystroke that would take me to the function definition in the browser.
Autoimports: meh. There are any number of tools that can rationalize imports. In the end, its not enough to get me to switch.
Syntax checking: highlighting is sufficient for my needs.
All emacs keymappings suck. Why? Because without exception they only extend to editor itself. Emacs is productive because *everything* in the editor uses the keymapping. The shell, the directory browser, the compiler output... everything. Emacs is much more integrated than any so-called IDE, because everything is a buffer and they all act the same way. I can run a macro that iterates a list of files in a directory (or subdirectories for that matter), performing a series of operations on each one, without every leaving emacs. In the end the sum of this approach is much more valuable than any collection of little features (most of which I have anyway, and just don't use).
Example: what do you need to do in IntelliJ to edit files that can only be accessed by FTP? Or how about viewing or editing files in a .jar contained in a .war contained in a .ear? How about running a macro across, say, all of the .tld files in a nested jar? Emacs does all of this transparently.
And lets go one step further. Emacs has the same sort of features available for Perl, SQL, C, shell script, you name it. All of which I use on a daily basis. Switching to the SQL IDE or the C++ IDE or whatever is a productivity killer when emacs treats them all the same.